Question

A rubber cord catapult has cross-sectional area $25m{m}^2$ and initial length of rubber cord is $10cm.$ It is stretched to $5cm$ and then released to project a missile of mass $5g$. Taking $Y_{\text{rubber }}=5\times 10^{8}N{m}^{-2}$, velocity of projected missile is

• A. $20m{s}^{-1}$
• B. $100m{s}^{-1}$
• C. $250m{s}^{-1}$
• D. $200m{s}^{-1}$

Answer 1

Answer: (C)

Potential energy stored in the rubber cord catapult will be converted into kinetic energy of mass.
$\frac{1}{2}m{v}^2=\frac{1}{2}\frac{YA{l}^2}{L}$
$\Rightarrow v=\sqrt{\frac{YA{l}^2}{mL}}$
$=\sqrt{\frac{5\times 10^8\times 25\times 10^{-6}\times {\left(5\times 10^{-2}\right)}^2}{5\times 10^{-3}\times 10\times 10^{-2}}}$
$=250m{s}^{-1}$