Question

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 $0.02\,kg$ on it and stretches the cord by $20\, cm$ by applying a constant force. When released, the stone flies off with a velocity of $20\, ms^{-1}$. 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)

$10^6 \; N/m^{-2}$

Answer 2

Energy of catapult $= \frac{1}{2} \times ( \frac{\Delta \ell}{\ell})^2 \times Y \times A \times \ell$

= Kinetic energy of the ball $= \frac{1}{2} mv^2$ therefore,

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

$Y \simeq3 \times10^{6} Nm^{-2}$