A) \[20m{{s}^{-1}}\]
B) \[100m{{s}^{-1}}\]
C) \[250m{{s}^{-1}}\]
D) \[200m{{s}^{-1}}\]
Correct Answer: C
Solution :
[c] Young?s modulus of rubber, \[{{Y}_{rubber}}=\frac{F}{A}\times \frac{\ell }{\Delta \ell }\Rightarrow F=YA.\frac{\Delta \ell }{\ell }\] On putting the values from question, \[F=\frac{5\times {{10}^{8}}\times 25\times {{10}^{-6}}\times 5\times {{10}^{-2}}}{10\times {{10}^{-2}}}=6250N\] kinetic energy = potential energy of rubber \[\frac{1}{2}m{{v}^{2}}=\frac{1}{2}F\Delta \ell \] \[v=\sqrt{\frac{F\Delta \ell }{m}}=\sqrt{\frac{6250\times 5\times {{10}^{-2}}}{5\times {{10}^{-3}}}}=\sqrt{62500}\] \[=250m/s\]
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