A uniform chain of length \(L\) and mass \(M\) is lying on a smooth table and one-third of its length is hanging vertically down over the edge of the table. If \(g\) is acceleration due to gravity, the work required to pull the hanging part on the table is:

1. \(MgL\)

2. \(MgL/3\)

3. \(MgL/9\)

4. \(MgL/18\)

Subtopic:  Gravitational Potential Energy |
 73%
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If W1, W2 and W3 represent the work done in moving a particle from A to B along three different paths 1, 2 and 3 respectively (as shown) in the gravitational field of a point mass m, find the correct relation between W1, W2 and W3 

(1) W1 > W2 > W3

(2) W1 = W2 = W3

(3) W1 < W2 < W3

(4) W2 > W1 > W3

Subtopic:  Gravitational Potential Energy |
 88%
From NCERT
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The displacement x of a particle moving in one dimension under the action of a constant force is related to the time t by the equation t=x+3, where x is in meters and t is in seconds. The work done by the force in the first 6 seconds is 

(1) 9 J

(2) 6 J

(3) 0 J

(4) 3 J

Subtopic:  Concept of Work |
 62%
From NCERT
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A force F=k(yi+xj) (where k is a positive constant) acts on a particle moving in the xy-plane. Starting from the origin, the particle is taken along the positive x-axis to the point (a, 0) and then parallel to the y-axis to the point (a, a). The total work done by the force on the particle is:

1. 2ka2

2. 2ka2

3. −ka2

4. \(ka^2\)

Subtopic:  Work Done by Variable Force |
 57%
From NCERT
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A lorry and a car moving with the same K.E. are brought to rest by applying the same retarding force, then:

1. Lorry will come to rest in a shorter distance

2. Car will come to rest in a shorter distance

3. Both will come to rest in a same distance

4. None of the above

Subtopic:  Work Energy Theorem |
 64%
From NCERT
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A particle free to move along the x-axis has potential energy given by U(x)=k[1e-x2] for x+, where k is a positive constant of appropriate dimensions. Then 

(1) At point away from the origin, the particle is in unstable equilibrium

(2) For any finite non-zero value of x, there is a force directed away from the origin

(3) If its total mechanical energy is k/2, it has its minimum kinetic energy at the origin

(4) For small displacements from x = 0, the motion is simple harmonic

Subtopic:  Potential Energy: Relation with Force |
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The kinetic energy acquired by a mass m in travelling a certain distance d starting from rest under the action of a constant force is directly proportional to 

(1) m

(2) Independent of m

(3) 1/m

(4) m

Subtopic:  Concept of Work |
 62%
From NCERT
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An open knife edge of mass 'm' is dropped from a height 'h' on a wooden floor. If the blade penetrates upto the depth 'd' into the wood, the average resistance offered by the wood to the knife edge is 

(1) mg

(2) mg1hd

(3) mg1+hd

(4) mg1+hd2

Subtopic:  Gravitational Potential Energy |
 59%
From NCERT
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A body is moving along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to 

(1) t1/2

(2) t3/4

(3) t3/2

(4) t2

Subtopic:  Power |
 76%
From NCERT
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Two particles of masses m1 and m2 in projectile motion have velocities v1 and v2 respectively at time t = 0. They collide at time t0. Their velocities become v1' and v2' at time 2t0 while still moving in air. The value of (m1v1'+m2v2')(m1v1+m2v2) is 

1. Zero

2. (m1+m2)gt0

3. 2(m1+m2)gt0

4. 12(m1+m2)gt0

Subtopic:  Collisions |
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