Question

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

• A. $ 20\,ms^{-1}$
• B. $ 100\,ms^{-1} $
• C. $ 250\,ms^{-1}$
• D. $ 200\,ms^{-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{Y A l^{2}}{L} $
$\Rightarrow v =\sqrt{\frac{Y A l^{2}}{m L}} $
$= \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}}} $
$= 250\, ms ^{-1}$