Question

Work done for certain spring when stretched through $1mm$ is $10$ joule. The amount of work that must be done on the spring to stretch it further by $1mm$ is

• A. $30J$
• B. $40J$
• C. $10J$
• D. $20J$

Answer 1

The correct option is A $30J$

Potential energy stored in spring to stretch it through $x$ length from rest length=$\frac{1}{2}k{x}^2$

Hence $10J=\frac{1}{2}k({10}^{-3}{)}^2$

The potential energy stored in it when it is further stretched by $1mm=\frac{1}{2}k({10}^{-3}+{10}^{-3}{)}^2=40J$

Hence energy required to stretch it from $1mm$ to $2mm=40J-10J=30J$