Question

A spring stores $1$ J of energy for a compression of $1$ mm. The additional work to be done to compress it further by $1$ mm is

• A. 1 J
• B. 2 J
• C. 3 J
• D. 4 J
• E. 0.5 J

Answer 1

The correct option is C 3 J

Given,
$W_1=1J,x=1\times {10}^{-3}m$
k=? (where k= spring constant)
$W_1=\frac{1}{2}k{x}^2$
$=\frac{1}{2}\times k\times (1\times {10}^{-3}{)}^2$
$k=2\times {10}^6$
$W_2=\frac{1}{2}k{x}_1^2$
$=\frac{1}{2}\times 2\times {10}^6\times (1\times {10}^{-3}+1\times {10}^{-3}{)}^2$
$W_2=4\times {10}^{-6}\times {10}^6=4J$
The additional work done $=W_2-W_1$
$=(4-1)J=3J$