Mechanical Properties of Solids

JEE Main level, single correct, medium

71 of 118

Question 71 of 118

A boy’s catapult is made of rubber cord which is 42cm42cm long, with 6mm6mm diameter of cross-section and of negligible mass. The boy keeps a stone weighing 0.02kg0.02kg on it and stretches the cord by 20cm20cm by applying a constant force. When released, the stone flies off with a velocity of 20ms−120m{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:

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Answer: (A) 106Nm−2{10}^{6}N{m}^{-2}

Elastic potential energy =12.Y.(∆lL)2AL=\dfrac{1}{2}.Y.{\left(\dfrac{∆l}{L}\right)}^{2}AL
=12Y.(0.20.42)2.(π×32×10−6×0.42)=\dfrac{1}{2}Y.{\left(\dfrac{0.2}{0.42}\right)}^{2}.\left(\pi \times {3}^{2}\times {10}^{-6}\times 0.42\right)
=(1.35×10−6)Y=\left(1.35\times {10}^{-6}\right)Y
Kinetic energy =12mv2=12×(0.02×(20)2)=\dfrac{1}{2}m{v}^{2}=\dfrac{1}{2}\times (0.02\times {\left(20\right)}^{2})
(1.35×10−6)Y=4\left(1.35\times {10}^{-6}\right)Y=4
Y=3×106Nm−2Y=3\times {10}^{6}N{m}^{-2}

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