Work - Power & Energy and Centre of Mass

Name : Roll No. : Topic :

Mohammed Asif

Ph : 9391326657, 64606657

WORK – POWER & ENERGY AND CENTRE OF MASS CONSERVATION OF MOMENTUM, COLLISIONS SECTION – I I.

This section contains 9 multiple – choice questions numbered 1 to 9. Each question has 4 choice (A), (B), (C), and (D), out of which Only One is correct.

1.

A particle of mass m is kept at the edge of a smooth cube of mass M and side L as shown in figure. Cube starts moving at t = 0 with a constant velocity v. Displacement of the center of mass along the horizontal direction from t = 0 to when particle hits the ground is m M

L 2L   +  g   v Mv  L 2L  C)  +  m + M  v g  A)

2.

s m

o o t h

v 2L   +  g   L Mv  v 2L  D)  +  m + M  L g 

mv m+ M

B)

mv m+ M

There are two masses M1 and M2 placed at a distance l apart, Let the centre of mass of this system is at a point named C. If M1 is displaced l 1 towards C and M2 is displaced by l 2 away from C. The distance from C where the new centre of mass will be located is M2 l 1 + M1 l 2 A) M1 + M2 M1 l 1 − M2 l 2 C) M1 + M2

3.

v

B) C)

M1 l 1 + M2 l 2 M1 + M2 M2 l 1 − M1 l 2 M1 + M2

In a boat of mass 4M and length ‘L’ on a frictionless water surface. Two men A(mass = M) B( mass = 2M) are standing on the opposite ends. Now A travels a distance L/4 relative to boat towards its centre and B moves a

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distance 3L/4 relative to boat and meet A. The displacement of he boat on water till A and B meet is 5L L 23L A) B) zero C) D) 28 2 2 4. A paraboloid shaped solid object is formed by Y rotating on parabola y = 2x 2 about y – axis as shown in figure. If the height of the body is ‘h’ then the position of h centre of mass O from origin. (Assume density to be uniform x throughout). h 2h h 2h A) B) C) D) 4 4 3 3 5. A pendulum of mass ‘m’ and length ‘1’ is m released from rest in a horizontal position. A nail at a distance ‘d’ below the pivot causes the mass to move to along the path as indicated by dotted lines. Find the minimum distance d in terms of l such that the mass will swing completely round in the circle shown 3l 2 l 3l A) B) C) D) l 4 3 2 5 6. A particle of mass m and speed v collides elastically with the end of a free uniform thin rod of mass M in a horizontal plane as shown. After the collision, m is stationary. Calculate M. A) m B) 2m C) 3m D) 4m 7.

l d

m v

( T o p

v i e w

)

M

Two small balls A and B of mass M and 3M respectively hang from the ceiling by ideal strings of equal lengths. The A ball is drawn aside so that it is raised to a height H. If the ball A is released and collides with ball B; Select the correct answer (s). A) If collision is perfectly elastic, ball B will rise to a height H/4 B) If the collision is perfectly elastic ball A will rise upto a height H/4 C) If the collision is perfectly inelastic, the combined A mass will rise to a height H/16 H B D) If the collision is perfectly inelastic, the combined Flat No.301, Rukkus & Yellus Arcade, Fever Hospital Road, Barkathpura, Hyd-500065. Ph: 040 – 64606657, 9391326657.

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mass will rise to a height H/4 8. There are two observers A and B, observer A C s m o o t h B is fixed to m the smooth plank and observer B is p l a standing on smooth horizontal ground. The plank is accelerated with constant acceleration, and C is placed on it then A) Momentum of block C is conserved as seen by observer A B) Momentum of block C is conserved as seen by observer B C) Net force on plank is zero as seen by observer A D) Net force on plank is non-zero as seen by observer B

A n

k

a

s m

o

9. The figure shows two blocks of mass 2 kg 4 m 2 / s 8 m 2 / s 1 k gs m o o 2 k g and 1 kg accelerating at 4 m/s2 and 8 m/s2 respectively starting from rest as shown in the figure, then which of the following are true at any instant (before the collision). r r r r A) a CM = 0 B) vCM ≠ 0 C) position of centre of mass is constant D) position of centre of mass is not constant

o

t h

t h

SECTION – II Assertion – Reason Type I. This section contains 4 questions numbered 10 to 13. Each question contains STATEMENT – 1 (Assertion) and STATEMENT – 2 (Reason). Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. NOTE: A. Statement – 1 is True, Statement – 2 is True; Statement – 2 is a correct explanation for Statement – 1. B. Statement – 1 is True, Statement – 2 is True; Statement – 2 is NOT a correct explanation for Statement – 1. C. Statement – 1 is True, Statement – 2 is False. D. Statement – 1 is False, Statement – 2 is True.

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10.

A rod is in contact with a wedge which is kept on the ground and can move only along its length between rigid supports as shown. If all the surfaces are smooth and the system is released from rest, then

STATEMENT – 1: - The mechanical energy of the system during the motion will be conserved. STATEMENT – 2: - The momentum of the system along horizontal direction is not conserved. 11. STATEMENT – 1: - The centre of mass of a system of particles is independent of coordinate system. STATEMENT – 2: - The centre of mass of system of two particles always divides the line joining them in the inverse ratio of their masses. 12. STATEMENT – 1: - On the application of impulse, the body will always move along the direction of the impulse. STATEMENT – 2: - Change in momentum is always along the direction of impulse. 13. STATEMENT – 1: - Kinetic energy of a system can be increased without applying any external force on the system. STATEMENT – 2: - Single external force acting on a particle necessarily changes its kinetic energy.

I.

SECTION – III Linked Comprehension Type

This section contains 2 paragraphs P14-16 , and P17-19 . Based upon each paragraph, 3 Multiple – choice questions have to be answered. Each question has 4 choices (A), (B), (C), and (D), out of which Only One is correct. P14 - 16 : Paragraph for Questions Nos. 14 to 16

A light inextensible thread passes over a small frictionless ideal pulley. Two blocks of masses m = 1 kg and M = 3 kg respectively are attached with the thread as shown in the figure. The heavier block rests on a horizontal surface. A shell of mass 1

A

m 3 00

M

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kg moving upward, parallel to incline, with a velocity 10 ms -1 collides at t = 0 and sticks to m. The combined mass travels up the incline to a distance s, stops for a moment and then moves down the incline. When the moving mass reaches its initial position, the string becomes taut and the mass M starts to climb up with an initial speed v 0. The mass M moves up to a height h before stopping momentarily. The inclined plane is smooth and along. The acceleration due to gravity is g = 10 m/s2 Answer the following questions: 14. 15. 16.

The value of s is: A) 1. 5 m B) 2. 0 m

C) 2. 5 m

D) 1. 0 m

The value of v0 is: A) 1. 0 m/s B) 2. 0 m/s

C) 2. 5 m/s

D) 5. 0 m/s

The value of h is: A) 0. 5 m B) 1. 0 m

C) 2. 0 m

D) 2. 5 m

P17 - 19 : Paragraph for Questions Nos. 17 to 19 A circular platform of mass 100 kg is placed symmetrically on a square frame of side 4m having four legs. The radius of the platform is 5m. 17. The maximum permissible mass of a dancer so that the platform does not topple is A) 33. 3 kg B) 66. 7 kg C) 50 kg D) 75 kg 18.

The area on the platform on which any mass of the dancer is permissible is A) 16 m2 B) 78. 5 m2 C) 8 m2 D) 62. 5 m2

19.

If five dancers are there on the stage each of mass 40 kg then the maximum number of dancer that can go together at same position along the circumference of the stage with the remaining staying at the centre so that the platform does not topple is A) 1 B) 2 C) 3 D) 4

SECTION – IV Matrix Match Type

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This section contains 3 questions. Each question contains statement given in two columns which have to be matched. Statement (A, B, C, D) in Column I have to be matched with statements (p, q, r, s) in Column II. The answers to these questions have to be appropriately bubbled as illustrated in the following example. If the correct matches are A-p, A-s, Bq, B-r, C-p, C-q and D-s, then the correctly bubbled 4 X4 matrix should be follows: 20.

p

q

r

s

A B C D

When a body is moving vertically up with constant velocity under the action of a lifting force and air resistance is absent. Column - I Column - II Work done by lifting force (p) Negative Total work done by all the (q) Positive forces C Work done by gravity (r) Zero D If air resistance starts (s) Non zero acting then work done by air resistance if it acts opposite to motion. A ball strikes the ground at an angle α and rebound at an angle β with the vertical as shown in figure. Then match the column I with column II from the combinations shown: A B

21.

A

Column - I Elastic collision

(p)

Column - II tan α α≠β tan β

B

Perfectly inelastic collision

(q)

α