Question

The potential energy of a certain spring when stretched through a distance ${}^{\prime }{S}^{\prime }$ is $10joule$. The amount of work (joule) that must be done on this spring to stretch it through an additional distance ${}^{\prime }{S}^{\prime }$ will be

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

Answer 1

Answer: (A)

$30$

Potential energy at displacement $S=10J$

For a spring $U_1=\frac{1}{2}k{s}^2$

To stretch spring from $s$ to $2S$

$U_2=\frac{1}{2}{\left(2S\right)}^2=4\left(\frac{1}{2}k{s}^2\right)$

Work done

Potential energy at displacement $S=10J$

For a spring $U_1=\frac{1}{2}k{s}^2$

To stretch spring from $s$ to $2S$

$U_2=\frac{1}{2}{\left(2S\right)}^2=4\left(\frac{1}{2}k{s}^2\right)$

Work done $U_2-U_1=(4-1)\left(\frac{1}{2}k{s}^2\right)=3\left(\frac{1}{2}k{s}^2\right)=3U_1=30J$