Two equal masses are attached to the two ends of a spring of spring constant k. The masses are pulled out symmetrically to stretch the spring by a length x over its natural length. The work done by the spring one each mass is

Options

A. `1/2 kx^2`
B. `-1/2 kx^2`
C. `1/4 kx^2`
D. `-1/4 kx^3`

Answer

D

Explanation

Negative work done on both masses = increase in potential energy of the spring.
`implies -2v = 1/2 kx^2 implies w = -1/4 kx^2`
Alternatively: Let both the blocks has been displaced by s
`implies` restoring force of the Spring is K(2s)
`implies` Work done on each block `= int_(0)^(x//2) k (2s) ds cos 180^@ = - (kx^2)/4`