question_answer

A boy's catapult is made of rubber cord which is 42 cm long, with 6 mm diameter of cross-section and of negligible mass. The boy keeps a stone weighing 0.02kg on it and stretches the cord by 20 cm by applying a constant force. When released, the stone flies off with a velocity of \[20m{{s}^{-1}}.\]Neglect the change in the area of cross-section of the cord while stretched. The Young's modulus of rubber is closest to:                                         [JEE Main 8-4-2019 Morning]

A) \[{{10}^{4}}\,N{{m}^{-2}}\] 

B)      \[{{10}^{8}}\,N{{m}^{-2}}\]

C) \[{{10}^{6}}\,N{{m}^{-2}}\] 

D)      \[{{10}^{3}}\,N{{m}^{-2}}\] Correct Answer: C Solution : [c] Energy of catapult\[=\frac{1}{2}\times {{\left( \frac{\Delta \ell }{\ell } \right)}^{2}}\times Y\times A\times \ell \]

= Kinetic energy of the ball\[=\frac{1}{2}m{{\text{v}}^{2}}\]

therefore,

\[\frac{1}{2}\times {{\left( \frac{20}{42} \right)}^{2}}\times Y\times \pi \times {{3}^{2}}\times {{10}^{-6}}\times 42\times {{10}^{-2}}=\]

\[\frac{1}{2}\times 2\times {{10}^{-2}}\times {{(20)}^{2}}\]

\[Y\simeq 3\times {{10}^{6}}N{{m}^{-2}}\]