A force \(F\) is applied to a system of two blocks: as shown in the figure. There is no friction between the lower block and the table. Due to friction between the blocks of masses \(m\) and \(M,\) they move together through a distance \(x.\)

     
Then work done by \(F\) on \(m\) is:

1. \(\dfrac{Fx}{2}\) 2. \(\dfrac{m}{m+M}Fx\)
3. \(\dfrac{M}{M+m}Fx\) 4. none of the above
Subtopic:  Concept of Work |
Level 4: Below 35%
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Given below are two statements: 
Statement I: The magnitude of the momentum of a body is directly proportional to its kinetic energy.
Statement II: Kinetic energy increases whenever an external force acts on a moving body.
 
1. Statement I is incorrect and Statement II is correct.
2. Both Statement I and Statement II are correct.
3. Both Statement I and Statement II are incorrect.
4. Statement I is correct and Statement II is incorrect.
Subtopic:  Concept of Work |
Level 3: 35%-60%
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A heavy uniform rope of mass \(m\) and total length \(L\) is slowly pulled down from the edge of a horizontal table, which exerts a frictional force on the rope, against its motion. The work done by pulling force is \(W_F\) and the work done against friction is \(W_f-\) both during the same time interval. The entire rope remains taut during its displacement. Then,
1. \(W_F=W_f\)
2. \(W_F>W_f\)
3. \(W_F<W_f\)
4. any of the above may be true depending on the coefficient of friction.
Subtopic:  Concept of Work |
Level 3: 35%-60%
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