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. $5\times {10}^{4}N{m}^{-2}$
• B. $4\times {10}^{8}N{m}^{-2}$
• C. $3\times {10}^{6}N{m}^{-2}$
• D. $2\times {10}^{3}N{m}^{-2}$

Answer 1

The correct option is C $3\times {10}^{6}N{m}^{-2}$

Increase in kinetic energy of catapult is converted into kinetic energy of the stone.
$\frac{1}{2}\times {\left(\frac{△l}{l}\right)}^2\times Y\times A\times l=\frac{1}{2}m{v}^2$
Therefore,
$\frac{1}{2}\times {\left(\frac{20}{42}\right)}^2\times Y\times \pi \times 3^2\times {10}^{-6}\times 42\times {10}^{-2}$
$=\frac{1}{2}\times 2\times {10}^{-2}\times (20{)}^2$
$⟹Y\simeq 3\times {10}^{6}N{m}^{-2}$