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

Answer 1

Answer: (D)

$- \frac { 1 } { 4 } k x ^ { 2 }$

Answer 2

If the spring is stretched by length x, then work done by two equal masses = $\frac { 1 } { 2 } k x ^ { 2 }$

So work done by each mass on the spring = $\frac { 1 } { 4 } k x ^ { 2 }$

∴ Work done by spring on each mass = $- \frac { 1 } { 4 } k x ^ { 2 }$.