A) \[20\,m{{s}^{-1}}\]
B) \[100\,m{{s}^{-1}}\]
C) \[250\,m{{s}^{-1}}\]
D) \[200\,m{{s}^{-1}}\]
Correct Answer: C
Solution :
Potential energy stored in the rubber cord catapult will be converted into kinetic energy of mass. \[\frac{1}{2}m{{v}^{2}}=\frac{1}{2}\frac{YA{{l}^{2}}}{L}\] \[\Rightarrow \] \[v=\sqrt{\frac{YA{{l}^{2}}}{mL}}\] \[=\sqrt{\frac{5\times {{10}^{8}}\times 25\times {{10}^{-6}}\times {{(5\times {{10}^{-2}})}^{2}}}{5\times {{10}^{-3}}\times 10\times {{10}^{-2}}}}\] \[=250\,m{{s}^{-1}}\]
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