DPP 15-17.pdf

PHYSICS Daily Practice Problems Target IIT JEE 2011 Class:XIII(X) Discussion: 11-12/08/2010 Time: 40 Min. M.M.: 34 DPP. NO.-15 Q.1 A block of mass 10 kg is released on a fixed wedge inside a cart which is moved with constant velocity 10 m/s towards right. Take initial velocity of block with respect to cart zero. Then work done by normal reaction on block in two second m ground frame will be: ( g = 10 m/s2) [3] (A) zero (B) 960 J (C) 1200 J (D) none of these   Q.2 A force F = (3tˆi  5ˆj) N acts on a body due to which its displacement varies as s  ( 2 t 2 ˆi  5ˆj) . Work ork done by this force in t = 0 to 2 sec is: [3] (A) 23 J (B) 32 J (C) zero (D) can’t be obtained. Q.3 A constant force produces maximum velocity V on the block connected to the spring of force constant K as shown in the fig. When the force constant of spring becomes 4K, the maximum velocity of the block is [3] V V (A) (B) 2V (C) (D) V 4 2 Paragraph for question nos. 4 to 6 The kinetic energy of any body depends on the frame of reference of the observer. The kinetic energy is given by 1/2 mv2rel. Similarly the displacement of the object from different frames of reference will be different. But the forces acting on the body remain unchanged. So work done by the forces as seen from different frames will be different. But work energy theorem will still be hold in every inertial reference frame. For example, if a block of mass 2 kg is moving with velocity of 1 m/s towards east on a rough surface, 1 its K.E. = × 2 × 12 = 1J 2 If it comes to rest, its K.E. = 0. Work done by friction = Kf – Ki = – 1 J If we observe it from a frame 2 moving with 1 m/s toward east, its initial velocity will appear to be 1–1=0. 1 Initial K.E. = × 2 × 02 = 0 2 Final velocity = 0 – 1 = –1 1 Final K.E. = × 2 × 12 = 1J 2  Work done by friction = 1 – 0 = 1 J Q.4

According to passage. (A) In 2nd frame, force of friction was opposite to displacement. (B) In 2nd frame, force of friction was in same direction as displacement. (C) In ground frame, force of friction is in same direction as the displacement. (D) None of these

Q.5

What should be the velocity of an observer so that he will report the work done by friction on the block to be 0. [3] 1 1 m/s W (B) m/s E (C) 1 m/s W 2 2 Choose correct statement. (A) In ground frame, work done by friction on ground is positive. (B) In ground frame, work done by friction on ground is negative. (C) In frame 2, work done by friction on ground is negative. (D) In frame 2, work done by friction on ground is positive.

(A) Q.6

[3]

(D) 1 m/s E [3]

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Q.7

Column-I shows certain situations and column-2 shows information about forces. Column - I Column - II

[6]

Situation F3

(A)

   (P) F1  F2  F3 is centripetal force.

F1 F2 Front view of a car rounding a curve with constant speed.  F1

 F3

• F2

(B) Passengers in a rotor not sliding relative to rotor wall cylindrical rotor is rotating with constant angular velocity about its symmetry axis.

  F3

(C)

 F1

 F2 Particle kept on rough surface of a bowl, no relative motion of particle in bowl, bowl has constant angular velocity

(D)

 (Q) F1 is static friction.

F3

 (R) F1 can be in direction opposite to that shown in figure.

   (S) F1  F2  0     (T) F1  F2  F3  0

F1  Car moving on a banked road with constant speed, no sideways skidding F2

Q.8 (a) (b) (c) (d)

(e)

A block of mass M is suspended from a massless ideal spring of spring constant k. The coordinate system is defined so that y is directed vertically upwards and y = 0 when the spring is at its natural (i.e., unstretched) length. The mass is first positioned at y = 0, and then lowered gently until it is hanging freely from the spring. What is the value of yeq, the coordinate of the point at which the block comes to rest? [10] When the block comes to rest, what is its gravitational potential energy Ug, compared to its value when the block was at y = 0? When the block comes to rest, what is the potential energy Us stored in the spring, compared to its value when the block was at y = 0? As the block was lowered from y = 0 to its equilibrium position, (i) What was the total work done on the block? (ii) What was the work done by gravity? (iii) What was the work done by the spring force? (iv) Was there any other agent that did work on the block? If so, what was it, and how much work did it do? If instead of being lowered gently the mass had simply been released from rest at y = 0 and allowed to fall under the combined effects of gravity and the spring force, at what speed would it be moving when it crosses y = yeq? PAGE # 2

PHYSICS Daily Practice Problems Target IIT JEE 2011 Class:XIII(X)

Discussion: 13-14/08/2010 Time: 35 Min.

M.M.: 29

DPP. NO.-16

Question No. 1 to 2 (2 questions) Figure gives the velocity v versus time t graph of a carriage of constant mass being moved along an axis by applying force. The time axis shows four time periods, with t1 = t2 = t3 and t4 = 2t1 Q.1 Q.2 Q.3

Q.4

Q.5

Q.6

Q.7

(a)

(b) (c) (d)

The work done by the force is maxmum during which time period [3] (A) t3 and t4 (B) t1, t3 and t4 (C) Only t3 (D) Only t4 The rate at which work done is maximum [3] (A) Only t1 (B) t1and t3 (C) Only t3 (D) Only t4 A man pulls a bucket of water from a well of depth h. If the mass of the uniform rope and bucket full of water are m and M respectively. The value of work done by the man is [3] m  mM  gh (A) (m+M) gh (B)   M  gh (C)  (D) None of the above 2   2  Choose the correct alternative(s): [4] (A) When a conservative force does positive work, the potential energy of the system decreases. (B) Work done by friction on a body always results in a loss of its kinetic energy. (C) Work done in the motion of a body over a closed loop is zero for every force in nature. (D) Work done by friction on a body may increase its kinetic energy. A spring having a relaxed length Lo = 25cm has a block attached to one end, while the other end is attached to a ceiling as shown. A person slowly k, L0 lowers the block a distance d until the block just hangs without moving, as m shown in the second diagram. Which statements below are true? (Mark ALL that apply. Use k = 2N/cm and m = 600g.) d (A) The distance d is 6cm. [4] (B) The potential energy stored in the spring when the block is simply hanging from it is 0.09J. (C) The change in gravitational potential energy of the Earth-block system is –0.18J. (D) The decrease in gravitational potential energy is equal (in magnitude) to the increase in potential energy stored in the spring. A block suspended from a spring is released from rest when spring is unstretched. ‘x’ represents stretch in spring. Select the appropriate graph taking quantities in column-I as y-axis. [6] 4 Column-I Column-II (A) The KE of block (P) 1 2 1 (B) The work done on the block by gravity (Q) 2 (C) The magnitude of work done on the block by spring (R) 3 3 (D) The total mechanical energy of block-earth-spring system (S) 4 xmax x A block of mass m rests on an incline which makes an angle  with the horizontal plane (see figure). There is friction between the block and the surface. The static friction coefficient s is larger than the kinetic friction coefficient k. The block is attached to a "massless" spring of spring constant k. In the absence of any forces on the spring, its (relaxed) length would be l. [6] We pull on the block and extend the spring till its length is l + x. What is the maximum extension, xmax, of the spring for which the block will remain stationary when released? In the following (b) & (c) parts, use the symbol xmax In this position the block is then gently touched at time t = 0. It starts moving. For what value of x will the block reach its maximum speed? As the block moves, the spring will get shorter. At some point in time, t1, the extension is x. How much work was done by (i) gravity, (ii) the spring force and (iii) by friction between t = 0 and t1. As the block moves up–hill, the spring gets shorter. What is a necessary requirement for the spring to PAGE # 3 become at least as short as its relaxed length l?

PHYSICS Daily Practice Problems Target IIT JEE 2011 Class:XIII(X) Discussion: 16-17/08/2010 Time: 35 Min. M.M.: 30 Q.1 In figure, a block of mass m is released from rest when spring was in its natural length. The pulley also has mass m but it is frictionless. Suppose the value of m is such that finally it is just able to lift the block M up after releasing it. [4] M g (A) The weight of m required to just lift M is 2 M (B) The tension in the rod, when m is in has zero acceleration g 2 M (C) The normal force acting on M when m has zero acceleration g 2 (D) The tension in the string when displacement of m is maximum possible is Mg Q.2

DPP. NO.-17 Rod String m M

A conservative force has the potential energy function U(x) as shown by the graph. A particle moving in one dimension under the influence of this force has kinetic energy 1.0J when it is at position x1. Which of the following is/are correct statement(s) about the motion of the particle ?

(A) It oscillates (B) It moves to the right of x3 and never returns (C) It comes to rest at either x0 or x2 (D) It cannot reach either x0 or x2

[4]

Q.3

Choose the correct option(s) (A) If only conservative forces act on a particle, the kinetic energy remains constant. (B) If the net force acting on an object is zero, then the object is at rest (C) If net mechanical work is done on a body, the body must accelerate (D) If net mechanical work is done on a body, the speed of body must change

[4]

Q.4

The spring is compressed by distance a and the system is released. The block again comes to rest when the spring is elongated by a distance b. During this process [3]

1 k (a  b ) 2 2 1 2 2 (B) work done by the spring on the block = k (a  b ) 2 k (a  b ) (C) coefficient of friction = 2mg k (a  b ) (D) coefficient of friction = 2mg

(A) work done by the spring on the block =

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Q.5

An endless inextensible string passes over two small smooth pegs A and B, AB being horizontal, two particles of mass M and m (M > m) are attached to the string. The particle of mass m is released when it is in level with the pegs. As it comes down M rises up vertically. If and when they cross each other [3]

(A) the speed of M > the speed of m (C) the speed of M < the speed of m Q.6

(B) the speed of M = the speed of m M (D) the ratio of their speeds is m

System shown in the figure is released from rest when spring is unstretched. Pulley and spring is massless and friction is absent everywhere. The speed of 5 kg block when 2 kg block leaves the contact with ground is (Take force constant of spring k = 40 N/m and g =10 m/s2) [3] (A)

2 m/s

(B) 2 2 m/s

(C) 2 m/s

(D) 4 2 m/s

Q.7

In the figure shown the spring constant is K. The mass of the upper disc is m and that of the lower disc is 3m. The upper block is depressed down from its equilibrium position by a distance  =5mg/K and released at t=0. Find the velocity of ‘m’ when normal reaction on 3m is mg. [3] 1/2 1/2 (A) zero (B) g[m/K] (C) 2g[m/K] (D) 4g[m/K]1/2

Q.8

Assume that in space potential energy U-depends on x-coordinate only by : [6] U = (x – 3)2 (2 – x) A mass m can be kept on x-axis. In each position indicated in column-I, comment on the situation from column-II. Column I Column II (A) x = 7/3 (P) Stable equilibrium (B)

x=2

(Q)

Unstable equilibrium

(C)

x=3

(R)

Neutral equilibrium

(S)

Not in equilibrium

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