Question

A rubber cord catapult has cross-section 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 $5gm$. Taking, $Y_{rubber}=5\times {10}^{8}N/m^2$, velocity of projected missile is

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

Answer 1

The correct option is C $250m{s}^{-1}$

Young's modulus of rubber, $Y_{rubber}=\frac{F}{A}\times \frac{l}{\Delta l}\Rightarrow F=YA\cdot \frac{\Delta l}{l}$
Thus, we get, $F=\frac{5\times {10}^8\times 25\times {10}^{-6}\times 5\times {10}^{-2}}{10\times {10}^{-2}}$
or, $F=25\times 25\times {10}^{2-1}=6250N$
Kinetic energy=Potential energy of rubber
Thus, $\frac{1}{2}m{v}^2=\frac{1}{2}F\Delta l$
or, $v=\sqrt{\frac{F\Delta l}{m}}=\sqrt{\frac{6250\times 5\times {10}^{-2}}{5\times {10}^{-3}}}=\sqrt{62500}$
Thus, $v=250m/s$