Q. 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 $5gm$. 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) $200\ ms^{- 1}$
Explanation
(c) Potential energy stored in the rubber cord catapult will be converted into kinetic energy of mass
$\frac{1}{2}mv^{2} = \frac{1}{2}\frac{YAl^{2}}{L} \Rightarrow v = \sqrt{\frac{YAl^{2}}{mL}}$
$= \sqrt{\frac{5 \times 10^{8} \times 25 \times 10^{- 6} \times \left( 5 \times 10^{- 2} \right)^{2}}{5 \times 10^{- 3} \times 10 \times 10^{- 2}}} = 250m/s$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.