A) \[\frac{a{{L}^{2}}}{2}+\frac{b{{L}^{3}}}{3}\]
B) \[\frac{1}{2}\left( \frac{a{{L}^{2}}}{2}+\frac{b{{L}^{3}}}{3} \right)\]
C) \[a{{L}^{2}}+b{{L}^{3}}\]
D) \[\frac{1}{2}(a{{L}^{2}}+a{{L}^{3}})\]
Correct Answer: A
Solution :
[a] Restoring force on rubber-band, \[F=ax+b{{x}^{2}}\]Work done in stretching the rubber-band by a small amount \[dx,dW=Fdx\] Net work done in stretching the rubber-band by L is \[W=\int{dW=\int\limits_{0}^{L}{Fdx=\int\limits_{0}^{L}{(ax+b{{x}^{2}})dx}}}\] \[\Rightarrow W={{\left[ a\frac{{{x}^{2}}}{2}+b\frac{{{x}^{3}}}{3} \right]}_{0}}^{L}=\frac{a{{L}^{2}}}{2}+\frac{b{{L}^{3}}}{3}\]
You need to login to perform this action.
You will be redirected in
3 sec
