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

Answer 1

Answer: (C)

3 J

Answer 2

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