Question

A block hangs freely from the end of a spring. A boy then slowly pushes the block upwards so that the spring becomes strain free. The gain in gravitational potential energy of the block during this process is not equal to
A. (a) The work done by the boy against the gravitational force acting on the block
B. (b) The loss of energy stored in the spring minus the work done by the tension in the spring
C. (c) The work done on the block by the boy plus the loss of energy stored in the spring
D. (d) The work done on the block by the boy minus the work done by the tension in the spring plus the loss of energy stored in the spring
(e) The work done on the block by the boy minus the work done by the tension in the spring

Answer 1

Correct Answer - A::B::D
Initially, the spring has an elongation, `DeltaL=mg//k`, where m is the mass of hanging block and k is the force constant of the spring. It means, initially spring has some strain energy. When the boy pushes the block upwards, the potential energy of the block increases and work is done by the boy during lifting of the block but spring becomes strain free. It means, initially, strain energy stored in spring is lost. Hence, the work done by the boy will be equal to increase in gravitational potential energy of the block minus loss in strain energy stored in the spring. Hence, only (c) is correct, i.e., all other options (a), (b), (d) and (e) are not correct.