A) \[8.7\times {{10}^{-2}}\text{J}\]
B) \[12.2\times {{10}^{-2}}\text{J}\]
C) \[8.7\times {{10}^{-4}}\text{J}\]
D) \[12.2\times {{10}^{-1}}\text{J}\]
Correct Answer: A
Solution :
Given, \[F=-5x-16{{x}^{3}}\] or \[F=-(5+16{{x}^{2}})x\] or \[F=-kx\] where \[k(=5+16{{x}^{2}})\] is force constant of spring. Therefore, work done in stretching the spring from position \[{{x}_{1}}\] to position \[{{x}_{2}}\] is \[W=\frac{1}{2}{{k}_{2}}x_{2}^{2}-\frac{1}{2}{{k}_{1}}x_{1}^{2}\] we have, \[{{x}_{1}}=0.1\,\,m\] and\[{{x}_{2}}=0.2\,\,m\] \[\therefore \] \[W=\frac{1}{2}[5+16{{(0.2)}^{2}}]{{(0.2)}^{2}}\] \[-\frac{1}{2}\,[5+16{{(0.1)}^{2}}{{(0.1)}^{2}}\] \[=2.82\,\times 4\times {{10}^{-2}}\,-2.58\,\times {{10}^{-2}}\] \[=8.7\,\times {{10}^{-2}}J\]
You need to login to perform this action.
You will be redirected in
3 sec
