Physics Assignment

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UNITS AND MEASUREMENT  CLASS XI PRACTICE ASSIGNMENT  DIMENSIONAL ANALYSIS:

1. Write Write the dimension dimensionss of of a and b in the relation relation P = (b-x 2)/a*t where P is power, x is distance and t is time. [M-1L0T 2], [L2] 2. In (P (P + a/ a/V2)*(V – b) = constant, P and V refer to pressure and and volume. Find the dimensions dimensions of a and b. [M1L5T -2], [L3] 3. Force Force (F) and and density density (d) are are relate related d as F = a/(b a/(b + √d). Find Find the dimension dimension of and b. 4. Check Check the correct correctness ness of the relation relation using using the method method of dimensions dimensions.. h = 2cos / r2dg where h is height,  is surface tension,  is angle of contact, r is radius , d is density and g is acceleration due to gravity 5. The Stoke’s Stoke’s formula for viscous force on a spherical spherical body may may depend depend upon its its radius (r), velocity of liquid (v) and the coefficient of viscosity (η). Find the formula dimensionally. [ F= kηrv] 6. The velocity velocity ‘v’ of water wave may depend upon upon wavelength wavelength ‘λ’, density density of water water ‘d’ and and acceleration due to gravity ‘g’. Derive the formula dimensionally. [k√λg] 7. The time of oscillation (t) of a small drop of liquid depends depends upon density density d, radius r and surface tension σ. Prove dimensionally that t = k (dr3/σ)1/2. 8. The time period T of oscillation of a gas bubble from an explosion explosion under water depends depends upon the static pressure (P), the density density of water (d) and the total energy (E) of explosion. explosion. Find the dimension of T dimensionally. [ T = K P -5/6d1/2E1/3] 9. The escape escape velocity velocity from the surface of the earth may depend upon the universal universal gravitational gravitational constant (G), mass of the earth (M) and the radius of the earth (R). Find the formula using the methods of dimensional analysis. [v = k √( √ (GM/R)] 10. The mass of the largest stone that can be moved by a flowing river river depends upon the velocity (v), the density of water (ρ) and acceleration due to gravity (g). Deduce the formula dimensionally. [kv6ρg-3] 11. A planet moves around around the sun in nearly circular circular orbit. Its period period of revolution ‘T’ depends depends upon radius of the orbit ‘r’, mass of the sum ‘M’ and the gravitational constant ‘G’. Show dimensionally that T 2 proportional proportional to r3. 12. Derive by the method of of dimensions an expression for the the volume of a liquid flowing per unit unit time through a narrow pipe. Rate of flow of liquid l iquid depends on coefficient of viscosity (η), the radius of the tube ( r) and pressure gradient (P/L). [kPr 4/ηL] 13. Deduce by the method of dimension an expression expression for the energy of the body executing S.H.M. assuming that energy depends upon the mass (m) of the body, the frequency (ν) of the body and the amplitude of vibration (a). [ E = K mv 2a2] 14. Reynolds’s number (R), (R), a constant depends upon upon velocity v, density  and coefficient of viscosity of the liquid (). Given that R varies varies directly as diameter diameter D of the pipe, derive derive the formula of R using the method of dimension [R = k ρvD/η ]

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15. By the method of dimension test the accuracy of the formula δ = mgl3 / 4b d3 Y, where δ is the depression produced in the middle of a bar of length l, breadth b and depth d, when it is loaded in the middle with mass m. Y is the Young’s modulus of the bar. 16. Find the dimensions dimensions of the quantity q from expression expression 3 T = 2π √ (m l / 3Yq) Where T is the time period of a bar magnet of length l, mass m and Young’s modulus Y. 17. If the speed of light c, Plank’s constant h and gravitational gravitational constant G are chosen chosen as fundamental fundamental units, find out the dimension dimension of mass, length and time. time. ERROR ANALYSIS:

18. Find the number number of significant figures in the the following: 3 24 (i) 0.007 m (ii) 2.64 x 10 kg (iii) iii) 0.237 .2370 0 gc gcm-3 (iv) 6.320 19. The length, breadth breadth and thickness of a rectangular sheet sheet of metal are 4.234 m, 1.005m and 2.01 cm respectively. Give the area and volume of the sheet to correct significant figure. [8.72 m2, 0.0855 m3] 20.If two resistors of resistances R1 = (4±0.5) Ω and R 2 = (16 ± 0.5) Ω are connected (i) in series and (ii) in parallel; find the equivalent resistances in each case with limits of percentage error. [ 20 Ω ± 5%, 3.2 Ω ± 3.3%] 21. The radius of a sphere is 1.41 cm. Express its volume to an appropriate appropriate number of significant figure. 22.1The length and breadth breadth of a rectangle are are (5.7 ± 0.1) cm and (3.4 ± 0.2) cm. Calculate area area of the rectangle with error limits. 23.A potential difference of V = (20 ± 0.5) volt is applied across a resistance of (8 ±2) ohm. Calculate the current with error limits. (V = I*R). 24.The measured value of length, l ength, breadth and height of a wooden block is given by L= 12.08 12. 08 ±0.01 cm, 10.12 ± 0.01 cm and h = 5.62 ± 0.01 cm. cm. Calculate the percentage error error in the volume of the block. [0.36 %] 25.Calculate the percentage error in specific s pecific resistance  = r2R/l where r = radius of the wire = (0.26 ± 0.02) cm l = length of the wire = (156.0 ± 0.1) cm R = resistance of the wire = (64 ± 2) ohm

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PHYSICS ASSIGNMENT CLASS XI CHAPTER 2: UNITS AND MEASUREMENT

1. Explain how you would use the parallax method to determine the distance of a planet from the earth using a neat diagram. 2. The radius of a sphere is 1.41 cm. Express its volume to an appropriate number of significant figure. [11.7 cm3] 3. An object is placed at a distance of (20.250 ± 0.010) cm from a convex lens and the image is obtained at a distance of (60.500 ± 0.050) cm from it on the other side of the lens. Calculate the focal length of the lens with its error.

[ (15.174 ± 0.009) cm]

4. In successive measurements, the readings of the period of oscillation of a simple pendulum were found to be 2.63 s, 2.56 s, 2.42 s, 2.71 s and 2.80 s in an experiment. Calculate (i) mean value of the period of oscillation (ii) absolute error in each measurement, (iii) mean absolute error, (iv) relative error and (v) percentage error. [ (i) 2.62 s, (iii)0.11 s, (iv) 0.04, (v) 4%] 5. Find the dimension of the quantity v in the equation v = {πP(a2 – x2) } / (2ηL) where, a is the radius and L length of the tube in which the fluid of coefficient of viscosity η is flowing, x is the distance from the axis and P is the pressure difference. [LT-1] 6. The period of vibration of a tuning fork depends on the length L of its prong, density d and Young’s modulus Y of the material. Deduce an expression for the period of vibration on the basis of dimensional analysis. [kL(d/Y)½] 7. The critical angular velocity ωc of a cylinder inside another cylinder  containing a liquid at which its turbulence occurs depends on viscosity η, density ρ and the distance d between the walls of the cylinder. Find an

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expression for ωc using the methods of dimension. [ Kη / ρd2]

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1. Thedisplacementofaparticlealongx-axisisgivenbyx=7t2+8t+3.Obtainthevelocity [36 m/s, 14 m/s2]

and acceleration at t = 2s.

2. Theaccelerationofaparticleinm/s2isgivenbya=3t2+2t+2,wheretimeisin seconds.Iftheparticlestartswithavelocityv=2m/satt=0,findthevelocityattheendof  2 seconds.

[18 m/s]

3. Thevelocity ofabodyatdifferenttimeintervalisgiveninthetable. T (seconds)

0

2

4

6

8

10

12

14

16

V (m/s)

5

10

15

15

20

25

20

10

0

Plotagraphshowingthevariationofvandt. Fromthegraph,find (i)

Accelerationbetween0and4seconds.

(ii)

Retardationbetween12and16seconds

(iii) Distancetraveledbythebodyduringfirst10secondsandlast4seconds. 4. Fromthetopofatower100minheightaballisdroppedandatthesametimeanother ballisprojectedverticallyupwardsfromthegroundsothatitreachesjustthetopofthe tower. At what height do the balls pass each other?

[ 75 m from the ground]

5. Aparachutistbailsoutfromanaeroplaneandafterdroppingthroughadistanceof40 m; heopenstheparachuteanddeceleratesatthe rateof2m/s2.Ifhe reachestheground withavelocityof2m/s,howlongisheintheair?Atwhatheightdidhebailoutfromthe plane?

[15.8 s, 235 m]

6. Aballisdroppedfromabridge122.5maboveariver.Aftertheballhasbeenfallingfor 2s,asecondballisthrownstraightdownafteritwhatmustbeitsinitialvelocitysothat both hit the water at the same time?

[26.1 m/s]

7. Therelationbetweentimetanddistancexisgivenbyt=αx2+βx,whereα,βare constants.Showthatretardationis2αv3,where‘v’istheinstantaneousvelocity. 8. Acaracceleratesfromrestataconstantrateofαforsometime;afterwhichit deceleratesataconstantrateofβtocometorest. Plotagraphtodepictthesame. Ifthe totaltimeelapsedisTseconds,thencalculate(i)maximumvelocityattainedbythecar, (ii)totaldistancetraveledbythecarintermsofα,βandT.

physicsacademy.co.in 9811119250 PHYSICS PRACTICE ASSIGNMENT  CLASS XI CHAPTER 4: MOTION IN A PLANE VECTORS 1. At what angle do the two forces (P + Q) and (P – Q) act so that the resultant is √ (3P2 + Q2)? [600] 2. A particle is acted upon by four forces simultaneously: (i) 30 N due east (ii) 20 N due north (iii) 50 N due west and (iv) 40 N due south. Find the resultant force on the particle. [20√2 N, 0 45 south of west] 3. Rain is falling vertically with a speed of 35m/s. After sometime wind started blowing at a speed of 12m/s in east to west direction. In which direction should a person hold an umbrella to avoid the rains? 4. A motorboat is racing towards north at 25km/h and water current at that region is 10km/h at 600 east of south. Find the resultant velocity of the boat. 5. The sum of magnitude of two forces acting at a point are 18 N and magnitude of their resultant is 12 N. If the resultant makes an angle of 90 0 with the force of smaller magnitude, what are the magnitudes of the two? [5 N, 13 N] 6. A man can swim with the speed of 4km/h in still water. How long does it take to cross the river 1 km wide, if the river flows steadily at 3 km/h and he makes his strokes normal to the river current? How far from the river does he go, when he reaches the other bank? [ 15 min, 0.75 km] 7. A man walking on a level road at a speed of 3 km/h. Rain drops fall vertically with a speed of 4 km/h. Find the velocity of the raindrops w.r.t the man. In which direction should he hold the umbrella? [ 5km/h, 360 52’] 8. A force of 7i + 6k N makes a body move on a rough plane with a velocity of 3j + 4k m/s. Calculate the power in watt. [24 W] 9. Determine a unit vector perpendicular to both A = 2i + j + k and B= I – j + 2k. [1/√3( i – j - k)] 10. Determine the sine of the angle between the vectors 3i + j +2k and 2i – 2 j + 4k. [2/√7] PROJECTILES 1. A person standing on the edge of a cliff 490m above the ground throws a ball horizontally with an initial speed of 15m/s. Find the time taken by the ball to reach the ground and the speed with which it hits the ground.( take g = 9.8 m/s2) [10s, 99.1 m/s] 2. A body is thrown horizontally from the top of a tower and strikes the ground after 3 seconds at an angle of 45 0 with the horizontal. Find the height of the tower and the speed with which the body was projected. Take g = 9.8 m/s 2. [44.1 m, 29.4 m/s] 3. A cricket ball is thrown at a speed of 28m/s in a direction 300 above the horizontal. Calculate (a) the maximum height (b) time taken by the ball to return to the same level and (c) the distance from the thrower where the ball lands. [ 10m, 2.9 s, 69.3 m] 4. A particle is projected with a velocity u so that its horizontal range is thrice the maximum height attained. What is the horizontal range? 5. Prove that the maximum horizontal range is four times the maximum height attained by the projectile, when fired at an inclination so as to have maximum horizontal range. 6. A boy stands at 78.4 m from a building and throws a ball which just enters a window 39.2 m above the ground. Calculate the velocity of projection of the ball. [39.2 m/s] 7. A hunter aims his gun and fires a bullet directly at a monkey in a tree. At the instant the bullet leaves the barrel of the gun, the monkey drops. Explain with proper mathematical reasoning whether the bullet will hit the monkey or not.

physicsacademy.co.in 9811119250 8. A ball thrown at an angle θ and another ball thrown at an angle (90° - θ) with the horizontal direction from the same point with velocity 39.2 m/s. The second ball reaches 50 m higher than the first ball. Find their individual heights. g = 9.8 m/s 2. [14.2 m, 64.2 m] 9. If R is the horizontal range for θ inclination and h is the maximum height reached by the projectile, show that the maximum range is given by (R 2/8h) + 2h. 10. From the top of a tower 156.8 m high a projectile is thrown up with a velocity of 39.2 m/s, making an angle 300 with the horizontal. Find the distance from the foot of the tower where it strikes the ground and the time taken by it to do so. [ 8s, 271.57 m] UNIFORM CIRCULAR MOTION 1. A stone tied to the end of a string 80 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 14 revolutions in 25 seconds, what is the magnitude and acceleration of the stone? [ 991.2 cm/s2] 2. A cyclist is riding with a speed of 27 km/h. As he approaches a circular turn on a road of radius 80 m, he applies brakes and reduces his speed at the constant rate 0.5 m/s. What is the magnitude and direction of the net acceleration of the cyclist on the circular turn? [ 0.86 m/s2, 54028’] 3. A body of mass 0.4 kg is whirled in a horizontal circle of radius 2m with constant speed of 10m/s. Calculate its (i) angular speed (ii) frequency of revolution (iii) time period and (iv) centripetal acceleration. [5 rad/s, 0.8 Hz, 1.25s, 50 m/s2] 4. Calculate the linear acceleration of a particle moving in a circle of radius 0.4 m at the instant when its angular velocity is 2 rad/s and its angular acceleration is 5 rad/s2. [2.6 m/s2, 38040’] 5. The angular velocity of a particle moving along a circle of radius 50 cm is increased in 5 minutes from 100 revolutions per minute to 400 revolutions per minute. Find (i) angular acceleration (ii) linear acceleration. [ (i) π/30 rad/s2, (ii) 5π/3 cm/s2]

physicsacademy.co.in 9811119250 PHYSICS PRACTICE ASSIGNMENT  CLASS XI CHAPTER 3: MOTION IN A LINE

1. A man walks on a straight road from his home to a market 2.5 km away with a speed of 5 km/h. Finding the market closed, he instantly turns and walks back home with a speed of 7.5 km/h. What is the (a) magnitude of average velocity and (b) average speed of the man over the interval of time (i) 0 to 30 min, (ii) 0 to 50 min and (iii) 0 to 40 min? [(i) 5km/h, 5km/h (ii) 0, 6 km/h (iii) 1.875 km/h, 5.625 km/h] 2. On a 60 km track, a train travels the first 30 km with a uniform speed of 30 km/h. How fast must the train travel the next 30 km or so as to average 40 km/h for the entire trip? [60 km/h] 3. A train moves with a speed of 30 km/h in the first 15 min, with another speed of 40 km/h the next 15 min and then with a speed of 60 km/h in the last 30 min. Calculate the average of the train during the journey. [47.5 km/h] 4. The displacement x of a particle varies with time t as x = 4t2 – 15t + 25. Find the position, velocity and acceleration of the particle at t=0. When will the velocity of the particle become zero? Can we call the motion of the particle as one with uniform acceleration? [25m, -15m/s, 8 m/s2, 1.875 s, Yes] 5. The velocity of a particle is given by the equation v = 2t2 + 5 cm/s. Find (i) the change in velocity of the particle during the time interval between t=2s and t= 4s (ii) the average acceleration during the same interval and (iii) the instantaneous acceleration at t= 4s. [ 24 cm/s, 12 cm/s2, 16 cm/s2] 6. A car moving along a straight highway with speed of 126 km/h is brought to stop within a distance of 200 m. what is the retardation of the car? How long does it take for the car to stop? [3.06 m/s2, 11.43 s] 7. On a foggy day two drivers spot each other when they are just 80m apart. They are travelling at 72 km/h and 60 km/h respectively. Both of them applied brakes retarding their cars at the rate of 5 m/s2. Determine whether they avert collision or not. [ Yes] th th 8. A body covers 20 m in 7 second and 24 m in 9 second. How much distance will it cover in 15 th seconds? [36 m] nd th 9. A body covers 12 m in 2 second and 20 m in 4 second. How much distance will it cover in 4 seconds after the fifth second? [136 m] 10. A stone falls from a cliff and travels 25 m in the last second before it reaches the ground at the foot of the cliff. Find the height of the cliff. Take g = 10 m/s2. [ 45 m] 11. A ball thrown up is caught by the thrower after 4 s. How high did it go and with what velocity was it thrown? How far was it below the highest point 3s after it was thrown? Take g = 10 m/s 2. [ 20 m/s, 20 m, 5 m] 12. A food packet is released from a helicopter which is rising steadily at 2 m/s. After 2 s (i) what is the velocity of the packet? (ii) How far is it below the helicopter? Take g = 10 m/s 2.[18 m/s, 20 m] 13. Two balls are thrown simultaneously, A vertically upwards with a speed of 20 m/s from the ground and B vertically downwards from a height of 40 m with the same speed and along the same line of motion. At what points do the balls collide? Take g = 10 m/s 2. [ after 1s at 15 m from ground] 14. A tennis ball is dropped on to the floor from a height of 4m. It rebounds to a height of 3 m. If the ball was in contact with the floor for 0.01 sec, what was the average acceleration during contact? g = 10 m/s2. [1669 m/s2] 15. A body falling from rest was observed to fall through 78.4 m in 2 sec. Find how long had it been falling before it was observed? Take g = 9.8 m/s 2. [3 second]

physicsacademy.co.in 9811119250 16. A ball is dropped from the roof of a tower of height ‘h’. The total distance covered by it in the last second of its motion is equal to the distance covered by it in the fir st 3s. What is the value of h? Take g =10 m/s 2. [125 m] 17. Two parallel rail tracks run north south. Train A moves north with a speed of 54 km/h and train B moves south with a speed of 90 km/h. what is the (i) Relative velocity of B w.r.t A? (ii) Relative velocity of ground with respect to B? (iii)Velocity of a monkey running on the roof of the train A against its motion with a velocity of 18 km/h with respect to train A as observed by a man standing on the ground? [ - 40 m/s, 25 m/s, 10 m/s] 18. Two trains A and B of length 400 m each are moving on two parallel tracks with a uniform speed of 72 km/h in the same direction, with A ahead of B. The driver of B decides to overtake A, and accelerates by 1 m/s 2. If after 50 s, the guard of B just brushes past the driver of A, what was the original distance between them? [ 1250 m] 19. The speed of motor launch with respect to still water is 7 m/s and the speed of stream is 3 m/s. when the launch began traveling upstream, a float was dropped from it. The launch traveled 4.2 km upstream, turned about and caught up with the float. After what time will the launch reach the float? [ 35 min] 20. A police van moving on a highway with a speed of 30 km/h fires a bullet at a thief’s car speeding away in the same direction with a speed of 192 km/h. If the muzzle speed of the bullet is 150 m/s, with what speed does the bullet hit the thief’s car? [105 m/s] 21. A balloon is ascending at the rate of 14m/s at a height of 98 m above the ground, when a packet is dropped from it. After how much time and with what velocity does it reach the ground? [6.12 s, 46 m/s] 22. From the top of a tower 100m in height a ball is dropped and at the same time another ball is projected vertically upwards from the ground so that it reaches just the top of the tower. At what height do the balls pass each other? [ 75 m from the ground] 23. A parachutist bails out from an aero plane and after dropping through a distance of 40 m; he opens the parachute and decelerates at the rate of 2m/s2. If he reaches the ground with a velocity of 2m/s, how long is he in the air? At what height did he bail out from the plane? [15.8 s, 235 m] 24. A ball is dropped from a bridge 122.5 m above a river. After the ball has been falling for 2s, a second ball is thrown straight down after it what must be its ini tial velocity so that both hit the water at the same time? [26.1 m/s]

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 Note: all bold letters are vectors or unit vectors.

1. and areunitvectorsalongthex-axisandy-axisrespectively.Whatisthemagnitude anddirectionofthevectors(i) + ,(ii)  –  ,(iii) ,(iv) x ? 2. Whydoesanarcherwhilethrowinganarrowatatargetalwaysaimsjustalittleabove thetarget? 3. Aballisthrownhorizontallywithvelocity‘u’andatthesametimeanotherballisdropped verticallyfromthetopofatowerofheight‘h’. (a) Willboththeballshitthegroundwithsametime? (b) Willboththeballsstrikethegroundwithsamevelocity? Justifyyouranswerineachcase. 4. Determineaunitvectorperpendiculartoboth =2 + + and =  –  +2 )] [1/√3( 5. Atwhichpointsontheprojectiletrajectoryisthe(i)potentialenergymaximum(ii)kinetic energyminimumand(iii)totalenergymaximum?Findtheenergiesattherespective points. 6. Thepositionofaparticleisgivenbyr=3t  –2t2 +4 m,wheretisinseconds. (a) Findtheinstantaneousvelocityandaccelerationoftheparticle. (b) Whatisthemagnitudeanddirectionofvelocityatt=2seconds?[8.54m/s,700withxaxis] 7. Ariver800mwideflowsattherateof5km/h. Aswimmerwhocanswimat10km/hin stillafter,wishestocrosstheriverstraight. (a) Alongwhatdirectionmusthestrike? (b) Whatshouldbehisresultantvelocity? (c) How much time he would take? [ 600withthebankofriver.8.66km/h,333.3sec] 8. Fromthetopofatower156.8mhighaprojectileisthrownupwithavelocityof39.2m/s, makinganangle300withthehorizontal.Findthedistancefromthefootofthetower where it strikes the ground and the time taken by it to do so. [ 8s,271.57m] 9. Atwhatangleshouldabodybeprojectedwithavelocity24m/sjusttopassoverthe obstacle16mhighatahorizontaldistanceof32m?Takeg=10m/s2 .[θ=670 54’or480 40’] 10. Astonetiedtotheendofastring80cmlongiswhirledinahorizontalcirclewith constantspeed.Ifthestonemakes14revolutionsin25seconds,whatisthemagnitude anddirectionofaccelerationofthestone? [9.9m/s2alongtheradiustowardsthecenter.]

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1. Explainwhy agunrecoilswhenabulletisfiredwithmathematicalexpressiontosupport youranswer. 2. Whydoesapersongethurtwhenhefallsfromacertainheightoncementedfloorbut doesn’tgethurtifhefallsonsandfromthesameheight? 3. Whathappenstotheapparentweightofamaninanelevatorwhenitis (i)

Movinguniformlyinupward/downwarddirection?

(ii) Acceleratingupwards, (iii) Acceleratingdownwards. 4. Thedriverofatrucktravellingwithvelocity‘v’suddenlynoticesawallinfrontofhimata distance‘d’.Shouldheapplythebrakesorshouldhemakeacircularturnwithout applyingbrakesinordertojustavoidcrashingintothewall?Justifyyouranswer. 5. Abulletofmass0.01kgisfiredhorizontallyintoa4kgwoodenblockatrestona horizontalsurface.Thecoefficientofkineticfrictionbetweentheblockandthesurfaceis 0.25.Thebulletremainsembeddedintheblockandthecombinationmoves20mbefore coming to rest. With what speed did the bullet strike the block?

[3969.7 m/s]

6. Twoblocksofmasses2kgand5kgareconnectedbyaninextensiblestringpassing overalightfrictionlesspulley.Theblockofmass2kgisfreetoslideonasurfaceinclined atanangleof300withthehorizontalwhereas5kgblockhangsfreely.Findthe accelerationofthesystemandthetensioninthestring.Givenμ=0.30. [a=4.87m/s2,T=24.65N]

7. Threebodiesofmassesm1,m2 andm3areconnectedas showninthefigure.Ifm1=5kg,m2=2kgandm3=3kg, calculatethetensions T1,T2andT3when (i) Thewholesystemismovingupwards withanaccelerationof2 m/s2,and (ii) Thewholesystemisstationary. Takeg=10m/s2 [120N, 60N,36N; 100N, 50N, 30N]

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PHYSICS PRACTICE ASSIGNMENT  CLASS XI CHAPTER 5: LAWS OF MOTION 1. A bird is sitting on the floor of a wire cage and the cage is in the hand of a boy. The bird starts flying in the cage. Will the boy experience any change in the weight of the cage? 2. Aeroplanes having propellers fly at low altitude while jet planes fly at high altitudes, why? 3. Why is it suggested that a gun must be held tightly with the shoulder while firing? 4. The speed of driving a car safely in darkness depends upon the range of headlights. Explain. 5. A retarding force is applied to stop a moving vehicle. If the speed of the vehicle is double of the original value, what distance will it cover before coming to rest under the same retarding force? 6. How does banking of roads reduce wear and tear of the tyres? 7. A hammer weighing 1 kg moving with a speed of 20m/s strikes the head of a nail driving it 10 cm into a wall. Neglecting the mass of the nail, calculate (a) the acceleration during the impact, (b) the time interval during the impact and (c) the impulse. [-2000 m/s 2, 0.01 sec, -20 Ns] 8. A monkey is ascending a branch with constant acceleration. If the breaking strength is 160% of the monkeys weight, what is the maximum acceleration permitted for the monkey? [a forceconstantofB.Inwhichspringismoreworkdoneiftheyarestretchedbysame amount? 4. Alightbodyandaheavybodyhavesame kineticenergies.Whichbodyhasthelarger linearmomentum? 5. AbodyofmassMatrestisstruckbya movingbodyofmassm.provethatthefractionof  itsinitialkineticenergyofmasstransferredtothestruckbodyis4Mm/(m+M)2. 6. Abulletofmass0.012kgandhorizontalspeed70m/sstrikesablockofwoodofmass 0.4kgandinstantlycomestorestwithrespecttotheblock.Theblockissuspendedfrom theceilingbyathinwire.Calculatetheheightuptowhichtheblockwillrise.Alsofindthe heat produced in the block.

[ 0.212 m, 28.54 J]

7. Themassofapendulumbobis0.2kganditissuspendedbyastring1mlong.Itis pulledasideuntilthethreadisat300tothevertical.Howmuchworkisdone?Thebobis nowreleased.Whatisitskineticenergyatthelowestpoint?Takeg=10m/s2. [ 0.268 J] 8. A60kgbungee-cordjumperisonabridge45maboveariver.Theelasticbungeecord hasarelaxedlengthof25m.AssumethatthecordobeysHooke’slaw,withaspring constantof160N/m. Ifthejumperstopsbeforereachingthewater,whatistheheightof  herfeetabovethewateratherlowestpoint?Takeg=10m/s2.

[ 2.05 m]

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CLASS ASSIGNMENT- PHYSICS CLASS XI WORK, ENERGY and POWER

1. A body is constrained to move along z-axis is subject to a constant force of F = -i + 2j +3k N, where i,j,k are the unit vectors along x-axis, y-axis and z-axis respectively. What is the work done by this force in moving the body by a distance of 4 m along z-axis? 2. What are the factors on which the spring constant of a spring depends? 3. Is it possible that a body is in accelerated motion under force acting on the body, yet no work is being done by the force? Give example. 4. A light body and a heavy body have same linear momentum. Which body has the larger K.E? 5. How are fast neutrons slowed down using moderators? 6. An aero plane’s velocity is doubled. What happens to its momentum and kinetic energy? 7. What will happen when (a) a heavy body collides with a light mass at rest, and (b) a light body collides with a heavy body at rest? 8. Two springs A and B are identical except that A is stiffer than B, i.e. force constant of A > force constant of B. In which spring is more work done if they are stretched by same force? 9. If the linear momentum of a body increases by 20%, what will be the % increase in the kinetic energy of the body? [44%] 10. If the kinetic energy of a body increases by 300%, what will be the % increase in the linear momentum of the body? [100%] 11. A particle of mass m is moving in a horizontal circle of radius r, under a centripetal force equal to –(K/r2), where K is constant. What is the total energy of the particle? [-K/2r] 12. A uniform chain of length 2m is kept on a table such that a length of 60 cm hangs freely from the edge of the table. The total mass of the chain is 4 kg. What is the work done in pulling the entire chain on the table? [3.6 J] 13. A pump on the ground floor of a building can pump up water to fill a tank of volume 30 m3 in 15 minute. If the tank is 40 m above the ground and the efficiency of the p ump is 30%, how much electric power is consumed by the pump? [ 43.567 KW] 3/2 14. A particle of mass 0.5 kg travels in a straight line with velocity v = ax where a = 5m -1/2 s-1. What is the work done by the net force during its displacement form x = 0 to x = 2m? [50 J] 15. A bullet of mass 10 g is fired with a velocity of 800 m/s. After passing through a mud wall 1m thick; its velocity decreases to 100 m/s. Find the average resistance offered by the wall. [3150 N] 16. When an automobile moving with a speed of 36 km/h reaches an upward inclined road of angle 30 0, its engine is switched off. If the coefficient of friction is 0.1, how much distance will the vehicle move before coming to rest? Take g = 10m/s 2. [8.53 m] 17. A shot traveling at the rate of 100 m/s is just able to pierce a plank 4 cm thick. What velocity is required to just pierce a plank 9 cm thick? [150 m/s] 18. The bob of a pendulum is released from horizontal position. If the length of the bob is 1.5 m, what is the speed with which the bob arrives at the lowest position? Assume 5% of the energy is lost due to air resistance. [ 5.3m/s]

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19. A ball of 0.1 kg makes an elastic head on collision with a ball of unknown mass that is initially at rest. If the 0.1 kg ball rebounds with one third of its original speed, what is the mass of the second ball? [0.2 kg] 20. A railway carriage of mass 9000 kg moving with a speed of 36 km/h collides with a stationary carriage of the same mass. After the collision, the carriages get coupled and move together. What is their common speed after collision? How much of the kinetic energy is lost during the collision? [5m/s, 225000 J] 21. A ball is dropped to the ground from a height of 2m. The coefficient of restitution is 0.6. To what height will the ball rebound? [ 0.72 m] 22. A sphere of mass m moving with a velocity u hits another stationary sphere of same mass. If e is the coefficient of restitution, what is the ratio of velocities of two spheres after collision? 23. A ball moving with a speed of 9 m/s strikes an identical ball at rest such that after collision the direction of each ball makes an angle 30 0 with the original line of motion. Find the speeds of the two balls after the collision. Is the kinetic energy conserved in the collision process? [3√3 m/s, No] 24. A car of mass 1000 kg moving on a horizontal road with a speed of 18 km/h collides with a horizontally mounted spring of spring constant 6.25 x 10 3 N/m. if the coefficient of friction is 0.5, calculate the maximum compression of the spring. Take g = 10m/s 2 [1.35 m]

25. Two blocks A and B are connected to each other as shown in the figure. The string and spring is mass less and pulley frictionless. Block B slides over the horizontal top surface of stationary block C and the block A slides along the vertical side of C both with same uniform speed. The coefficient of friction between the blocks is 0.2 and the spring constant is 2000 N/m, if the mass of block A is 2kg, calculate (i) the mass of block B and (ii) energy stored in the spring. Take g = 10 m/s2. [ 10 kg, 0.1 J] B

C

A

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CLASS ASSIGNMENT- PHYSICS CLASS XI SYSTEM OF PARTICLES AND ROTATIONAL MOTION 1. Why an ice skater or a ballet dancer does sometimes stretches their hands and sometimes brings them closer to the body while performing their routines? 2. If angular momentum is conserved in a system whose moment of inertia is decreased, will its rotational kinetic energy be also conserved? 3. Two circular discs A and B of the same mass and same thickness are made of two different metals whose densities are dA and dB (dA>dB). Their moments of inertia about the axes passing through their centres of gravity and perpendicular to their planes are IA and IB. Which is greater; IA or IB? 4. Torques of equal magnitude is applied to hollow cylinder and a solid sphere, both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry and the sphere is free to rotate about an axis passing through its centre. What is the ratio of their angular acceleration? 5. A ring, a disc and a sphere all of the same radius and mass roll down an inclined plane from the same height h. Which of the three reaches the bottom (i) earliest (ii) latest? 6. Three identical spheres each of radius ‘r’ and mass ‘m’ are placed touching each other on a horizontal floor. Locate the position of centre of mass of the system. [ r, r/√3] 7. Two particles of mass 2kg and 1kg are moving along the same straight line with speeds of 2m/s and 5m/s respectively. What is the speed of the centre of mass of the system if both the particles are moving (i) in same direction and (ii) in opposite direction? [ 3m/s, 1/3 m/s] 8. Four particles A,B, C and D of masses m,2m,3m and 4m respectively are placed at the corners of a square of side x with A being the origin of the co-ordinate axes and the square is in the 1st quadrant. Find the position of the centre of mass of the square. [x/2, 7x/10] 9. A circular disc has a mass M and radius R. How would the CM of the disc change if a circular portion of radius R/2 is cut from it? 10. What will be the duration of the day, if earth suddenly shrinks to 1/64 th of its original volume? [1.5 hr] 11. Energy of 484 J is spent in increasing the speed of a flywheel from 60 to 360 rpm. Calculate MI of flywheel. [0.7kgm2] 12. A disc of mass 5 kg and radius 50 cm rolls on the ground at the rate of 10m/s. Calculate the K.E. of the disc. (Given I = ½ MR 2). [375 J] 3 2 13. A particle starts rotating from rest according to the formula θ = 3t /20 – t /3. Calculate the angular velocity and angular acceleration after 5 seconds. [ 7.92 rad/s, 3.83 rad/s2] 14. A spherical ball rolls on a table without slipping. Determine the percentage of its K.E. which is rotational. M.I. of sphere = 2/5 MR 2. [28.57%] 15. A boy is seated in a revolving chair revolving at an angular speed of 120 rpm. By some arrangement, the boy decreases the moment of inertia of the system from 6 kgm2 to 2kgm2. What will be the new angular speed? [ 360 rpm] 16. A grindstone has moment of inertia 50 m.k.s. unit. A constant torque is applied and the grindstone is found to have a speed of 150 rpm, 10 seconds after starting from rest. Find the torque. [25π Nm]

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17. A flywheel rotating at the arte of 120 rpm slows down at a constant rate of 2 rad/s2. What time is required to stop the flywheel and how many rotations does it make in the process? [ 2π s, 2π rev] 18. A sphere of mass 2 kg and radius 5 cm is rotating at the rate of 300 rpm. Calculate the torque required to stop it in 6.28 revolutions. M.I of sphere = 2/5 MR2. [ 2.542 x 10 -2 Nm] 19. A flywheel of moment of inertia 5 kgm2 is rotated at a speed of 60 rad/s. Because of friction on the axle, it comes to rest in 5 minutes. Find (a) Average torque of the friction, (b) Total work done by the friction, (c ) Angular momentum of the wheel one minute before it stops rotating. [-1 N-m, 9kJ, 60 kgm2/s] 20. A flywheel of mass 1000 kg and radius 1m is rotating at the rate of 420 rpm. Find the constant retarding torque required to stop the wheel in 14 rotations, assuming mass to be concentrated at the rim. [10000 Nm] 21. A disc of mass 200 kg and radius 0.5 m is rotating at the rate of 8 revolutions per second. Find the constant torque required to stop the disc in 11 rotations. [ 457.01 N-m] 22. A solid cylinder of mass 20 kg rotates about its axis with angular speed of 100 rad/s. the radius of the cylinder is is 0.25 m. What is the kinetic energy associated with the rotation of the cylinder? What is the magnitude of the angular momentum of the cylinder about its axis? [31250 J, 62.5 Nms] 23. a cylinder of mass 5 kg and radius 30 cm and free to rotate about its axis, receives an angular impulse of 3 kgm2/s followed by a similar impulse after every 4 second. What is the angular speed of the cylinder 30 s after the initial impulse? The cylinder is at rest initially. [106.67 rad/s] 0 24. A solid cylinder rolls up an inclined plane of angle of inclination 30 . At the bottom, of the inclined plane the centre of mass of the cylinder has a speed of 5m/s. (i) How far will the cylinder go up the plane? (ii) How long will it take to return to the bottom? [3.8m, 3 sec]

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1. ThemomentsofinertiaoftworotatingbodiesAandBareI AandIB (I A>IB)andtheir angularmomentumareequal.WhichonehasgreaterK.E.? 2. Asphericalballrollsona tablewithoutslipping.DeterminethepercentageofitsK.E. whichisrotational.M.I.ofsphere=2/5MR2.

[28.57%]

3. Asolidsphererollsdowntwodifferentinclinedplanesofsameheightsbutdifferent anglesofinclination. (i) Willitreachthegroundwiththesamespeedineachcase? (ii) Willittakelongertorolldownoneplanethananother?Ifso,whichoneandwhy? 4. WhatisthemomentofinertiaofauniformcirculardiscofradiusRandmassMabout (i) Diameterofthedisc. (ii) Anaxispassingthroughapointonitsedgeandnormaltothedisc? (iii) Atangentintheplaneofthedisc M.I.aboutanaxispassingthroughitscentreandperpendiculartoitis½MR2. 5. Fromasquaresheetofuniformdensity,theshadedportionisremoved.Findthecentre ofmassoftheremainingportionifthesquarehasasideatakingtheorigintobelyingat  A.

[7/18a,a/2]

DC

AB 6. Acarweighs1800kg.Thedistancebetweenthefrontandbackaxleis1.8m.Itscentreof  gravityis1.05mbehindthefrontaxle.Determinetheforceexertedbythelevelground on each front wheel and back wheel. Take g = 9.8 m/s2.

[3675 N, 5145 ]

7. Asolidcylinderrollsdownaninclinedplane.Itsmassis2kgandradius0.1m,ifthe heightoftheinclinedplaneis4m,whatisitsrotationalK.E.atthebottomoftheincline? M.I.ofsolidcylinderaboutitsaxisis½MR2.

[26.13 J]

8. Acylinderofmass10kgandradius15cmisrollingperfectlyonaplaneofinclination 300.Thecoefficientofstaticfrictionis0.25. (a)Howmuchistheforceoffrictionactingonthecylinder? (b)Iftheinclinationθoftheplaneisincreased,atwhatvalueofθdoesthecylinder began to skid and not roll perfectly?

[16.4 N, θ = 37 0]

physicsacademy.co.in 9811119250

CLASS ASSIGNMENT- PHYSICS CLASS XI GRAVITATION

1. According to Newton’s law of gravitation, the apple and the earth experiences equal and opposite forces due to gravitation. So, why only the apple falls towards the earth and not the earth towards the apple? 2. The mass and the diameter of a planet are twice that of the earth. What will be the time period of that pendulum on this planet for a second’s pendulum at the earth? 3. Why do every falling body to the surface of the earth experience the same acceleration due to gravity? 4. If the diameter of the earth becomes twice the present value but its average density remains unchanged then how would be the weight of an object on the surface of the earth be affected? 5. Two artificial satellites, one close to the surface and the other away are revolving around the earth, which has larger speed and why? 6. In what way gravitation of a planet or satellite determine the existence of its atmosphere? 7. When a satellite moves to a lower orbit in the atmosphere of the earth, it becomes hot. This indicates that there is some dissipation of energy. But the satellite falls towards earth with increasing speed. Why? 8. Generally the path of a projectile from the earth is parabolic but it is elliptical for projectiles going to very great height. Why? 9. A person sitting on an artificial satellite feels weightlessness but a person standing on moon has weight though moon is also a satellite of the earth. Give reason. 10. A body weighs 64 N on the surface of the earth. What is the gravitational force on it, due to the earth, at a height equal to half the radius of earth? Acc. Due to gravity on the surface of the earth = 10 m/s. [28.44 N] 11. Two equal masses m and m are hung from a balance whose scale pans differ in vertical height h. Calculate the error in weighing, if any, in terms of density of earth. [8/3 Gmh] 12. Calculate the increase in the potential energy of an object of mass m raised from the surface of the earth to a height equal to the radius of the earth. [ ½ mgR] 13. To what height a mass can go, when sent up with a velocity of half the escape velocity? [R/3] 14. At what height above earth’s surface, value of g is same as in a mine 100 km deep? [ 50 km] 15. How much below the surface does the acceleration due to gravity become 70% of its value on the surface? Radius of the earth = 6.4 x 10 6 m. [ 1.92 x 106 m ] 16. Find the percentage decrease in the weight of a body when taken to a height of 16 km above the surface of the earth. Radius of the earth = 6400 km. [ 0.5 %] 17. A 400 kg satellite is in a circular orbit of radius 2R E about the earth. How much energy is required to transfer it to a circular orbit of radius 4R E? What are the changes in the kinetic and potential energies? [ 3.13 x 10 9 J, -3.13 x 109 J, 6.26 x 109 J] 18. Find the potential energy of a system of four particles each of mass m placed at the vertices of a square of side L. Also obtain the potential at the centre of the square. [-5.41 Gm2/L, -4√2 Gm/L] 19. Jupiter has a mass 318 times that of earth and its radius is 11.2 times that of earth. Estimate the escape velocity of a body from Jupiter’s surface, given that escape velocity from earth is 11.2 km/s. [59.7km/s]

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20. A Saturn year is 29.5 times that of earth year. How far is the Saturn from the Sun if the earth is 1.5x105 km away from the Sun [1.43 x 10 9 km] 21. A man can jump 1.5 m high on the earth. Calculate the approximate height he might be able to  jump on a planet whose density is 1/4 th and radius 1/3rd of earth’s surface. [ 18 m] 22. A body hanging from a spring stretches it by 1 cm at earth’s surface. How much will the same body stretch the spring at a place 1600 km above the earth’s surface? R = 6400 km. [ 0.64 cm] 23. At what height above the earth’s surface, the value of g is half of its value on earth’s surface? R = 6400 km. [2649.6 km] 24. A mass of 0.5 kg is weighed on a balance at the top of a tower 20 m high. The mass is then suspended from the pan of the balance by a fine wire 20 m long and is r eweighed. Find the change in weight. R = 6400 km. [3.125 x 10 -6 kgf] 25. At what height from the surface of the earth, will the value of g be reduced by 36% from the value at the surface? R = 6400 km. [ 1600 km] 26. Find the percentage decrease in weight of a body, when taken 16 km below the surface of the earth. R = 6400 km. [ 0.25%] 27. Find the work done to bring 4 particles each of mass 100 g from large distances to the vertices of a square of side 20 cm. [ -1.8 x 10 -11 J] 28. The escape velocity of a projectile on the earth’s surface is 11.2 km/s. A body is projected out with thrice this speed. What is the speed of the body far away from the earth? Ignore the presence of the sun and other planet. [31.68 km/s] 29. An artificial satellite revolves around the earth at a height of 1000 km. the radius of the earth is 6.38 x 10 3 km. mass of earth is 6 x 1024 kg and G = 6.67 x 10 -11 Nm2/kg2. Find the orbital velocity and period of revolution. [7364 m/s, 6297 s] 13 12 30. The distance of two planets from the sun is 10 and 10 m respectively. Find the ratio of time periods and speeds of the two planets. [ 1/√10]

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1. Showgraphicallyhow‘g’variesasyougofromthecentreoftheearthtogreat heightsabovethesurface. 2. Twosatellitesarerevolvinginsameorbit,withoneseparatedfromtheotherby distance’x’.Willthesecondsatellitebeabletoovercomethefirstbyincreasing itsspeed?Whyorwhynot? 3. Whenaclockcontrolledbyapendulumistakentoamountainitbecomesslow butawristwatchcontrolledbyaspringremainsunaffected.Explainthedifferent behaviourofthetwowatches. 4. Whenasatellitemovestoalowerorbitintheatmosphereoftheearth,itbecomes hot.Thisindicatesthatthereissomedissipationinitsmechanicalenergy.But thesatellitespillsdowntowardstheearthwithanincreasingspeed.Explain. 5. Calculatetheincreaseinthepotentialenergyofanobjectofmassmraisedfrom thesurfaceoftheearthtoaheightequaltodoubletheradiusoftheearthinterms of the acceleration due to gravity of the earth. [ 2/3mgR] 6. Twostarseachofonesolarmass(2x10 30kg)areapproachingeachotherfora headoncollision.Whentheyareatadistanceof109km,theirspeedsare negligible.Whatisthespeedwithwhichtheycollide?Theradiusofeachstaris 104km. Assumethestarstoremainundistorteduntiltheycollide.G=6.67x10-11 Nm2/kg2. [ 2.6 x 106m/s] 7. Two starsofmassesMand 16M areseparated byadistance10a. Theirradiiare respectively‘a’and‘2a’.Whatshouldbetheinitialvelocitywithwhichamassm be fired from larger star to land on the smaller star? [3/2√(5GM/a)] 8. Arocketisfiredverticallyfromthesurfaceofthemarswithspeedof2km/s. If  20%ofitsinitialenergyislostduetomartianatmosphericresistance,howfarwill therocketgofromthesurfaceofmarsbeforereturningtoit?Massofmars=6.4x 1023 kg, radius of mars = 3400 km.

[1655 km]