Question

A rubber cord catapult has cross-sectional area $25m{m}^2$ and initial length of rubber cord is 10 cm 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. 20 $m{s}^{-1}$
• B. 100 $m{s}^{-1}$
• C. 250 $m{s}^{-1}$
• D. 200 $m{s}^{-1}$

Answer 1

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

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