# A rubber catapult has a cross sectional area $2mm^2$ and total unstretched length 15cm.It is stretched to 18cm and then released to project a missile of 3g.Taking young modulus $8\times 10^8N/m^2$ find velocity of projection?

$\begin{array}{1 1}(A)\;28m/s\\(B)\;56m/s\\(C)\;50m/s\\(D)\;\text{None of above}\end{array}$

When the projectile is projected the elastic potential energy of string change in kinetic energy of missile.
$\large\frac{1}{2}$$mv^2=\large\frac{1}{2}$$\times Y\times (strain)^2\times volume$
$v^2=\large\frac{Y\times (strain)^2\times volume}{m}$
$\;\;\;\;=\large\frac{8\times 10^8\times (3/15)^2\times 2\times 15\times 10^{-6}\times 10^{-2}}{3\times 10^{-3}}$
$\;\;\;\;=\large\frac{8\times 2\times 15\times 10^3}{5^2\times 3}$
$\;\;\;\;=\large\frac{16}{5}$$\times 10^3$
$\;\;\;\;=3200$
$v=56.56m/s$
Hence (B) is the correct answer.