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 is

(a) 1/2kx²

(b) -1/2kx²

(c) 1/4kx²

(d) -1/4kx².

Answer 1

(d)  -1/4kx².

Explanation:- 

The work done by the spring on both of the masses is equal to the potential energy stored in the spring. The potential energy stored in the spring = -½kx². 

Since the masses are pulled out symmetrically, the work done by the string on each mass

 =½(-½kx²) =-¼kx². 

The negative sign is for the fact that displacement is opposite to the force.