. An object is attached to a vertical spring and slowly lowered to its equilibrium position

This stretches the spring by a distance d. If the same object is attached to the same vertical spring but permitted to fall instead the spring will be stretched through a distance.

A. d/2

B. 3d/2

C. d/2

D. 2d

Best Answer

Correct option is D

If the spring is loaded and lowered slowly to the equilibrium position, the object has no kinetic energy and comes to rest with an extension d to the spring, which is equal to MG/K. When it is allowed to fall, it acquires a kinetic energy as it passes the equilibrium position and will oscillate about the equilibrium position.

Decrease in gravitational potential energy = increase in elastic potential energy