Question

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 on each mass during the above stretching 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 $-\frac{1}{4}k{x}^2$

total work done by spring will be (initial energy stored-final energy stored).

$W=0-\frac{1}{2}k{x}^2$

also spring will apply equal force on both the masses, work done on each mass is equal.

so work done per mass is given by $-\frac{1}{4}k{x}^2$

option D is answer.