Question

A stone of mass $20\text{g}$ is projected from a rubber catapult of length $0.1\text{m}$ and area of cross section ${10}^{–6}{\text{m}}^2$ stretched by an amount $0.04\text{m}$. The velocity of the projected stone is ____ $\text{m/s}$.
(Young's modulus of rubber $=0.5\times {10}^9\text{N}/{\text{m}}^2$)

Answer 1

By energy conservation, elastic potential energy gets converted into kinetic energy.

$\therefore \frac{1}{2}K{x}^2=\frac{1}{2}m{v}^2$

$\frac{1}{2}\frac{YA}{L}(\Delta L{)}^2=\frac{1}{2}m{v}^2$

where, $K=\frac{YA}{L};\Delta L=x$

$\frac{0.5\times {10}^9\times {10}^{-6}\times (0.04{)}^2}{0.1}=\frac{20}{1000}{v}^2$

$\Rightarrow v^2=400$

$\begin{array}{c}\therefore v=20\text{m/s}\end{array}$