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 $Y_{rubber}=5\times {10}^{8}N{m}^{-2}$, 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)

250 ms${}^{-1}$

Potential energy stored in the rubber cord catault will be converted into kinetic energy of mass
$\frac{1}{2}m{v}^2=\frac{1}{2}\frac{YA{l}^2}{L}$

where $l=5\times {10}^{-2}$m, $A=25\times {10}^{-6}{m}^2,$ $L=10\times {10}^{-2}$m, $m=5\times {10}^{-3}kg$
$\Rightarrow v=\sqrt{\frac{YA{l}^2}{mL}}$
$v=\sqrt{\frac{5\times {10}^8\times 25\times {10}^{-6}\times (5\times {10}^{-2}{)}^2}{5\times {10}^{-3}\times 10\times {10}^{-2}}}$
$v=250m{s}^{-1}$