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 $20m/s$. 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. ${10}^{3}N/m^2$
• C. ${10}^{6}N/m^2$
• D. ${10}^{8}N/m^2$

Answer 1

The correct option is C ${10}^{6}N/m^2$

Formula used: $U=\frac{1}{2}(\text{strain}{)}^{2}Y\times AL$,

strain$=\frac{\Delta l}{l}$

Given: $L=42cm,m=0.02kg,\Delta l=20cm,r=3mm$

Energy of catapult,

$U=\frac{1}{2}\times {\left(\frac{\Delta l}{l}\right)}^2\times Y\times A\times l$

The kinetic energy of the ball,

$K=\frac{1}{2}m{v}^2$

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

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

$Y\cong 3\times {10}^{6}N/m^2$

FINAL ANSWER: (c)