Question

A boy’s catapult is made of rubber cord which is $42cm$ long, with $6mm$ diameter of cross-section and of negligible mass. The boy keeps a stone weighing $0.02kg$ on it and stretches the cord by $20cm$ 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:

• A. $10^{4}N/m^{-2}$
• B. $10^{8}N/m^{-2}$
• C. $10^{6}N/m^{-2}$
• D. $10^{3}N/m^{-2}$

Answer 1

Answer: (C)

Energy of catapult $=\frac{1}{2}\times (\frac{\Delta \ell }{\ell }{)}^2\times Y\times A\times \ell$
= Kinetic energy of the ball $=\frac{1}{2}m{v}^2$ therefore,
$\frac{1}{2}\times {\left(\frac{20}{42}\right)}^2\times Y\times \pi \times 3^2\times 10^{-6}\times 42\times 10^{-2}=\frac{1}{2}\times 2\times 10^{-2}\times {\left(20\right)}^2$
$Y\simeq 3\times 10^{6}N{m}^{-2}$