Question

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

• A. $\frac{1}{2}k{x}^2$
• B. $-\frac{1}{2}k{x}^2$
• C. $\frac{1}{4}k{x}^2$
• D. $-\frac{1}{4}k{x}^2$

Answer 1

The correct option is D $-\frac{1}{4}k{x}^2$

work done by spring is =initial energy stored -final energy stored.

so work done by spring $=0-\frac{1}{2}k{x}^2$

force applied by spring on both the blocks is same so work done by spring will be evenly distributed among both the blocks.

so work done by spring on each block is $-\frac{1}{4}k{x}^2$.

so answer is D.