A catapult consists of two parallel rubber strings, each of lengths 10 cm and cross-sectional area 10 mm². When stretched by 5 cm, it can throw a stone of mass 100 g to a vertical height of 25 m. Determine Young's modulus of elasticity of rubber $\left(\text{ in }\times {10}^8 \mathrm{N}/{\mathrm{m}}^2\right)$.

A stretched catapult has elastic potential energy stored in it (elastic potential energy stored in both the rubber strings)

          $\mathrm{U}=\left(\frac{1}{2}\frac{{\mathrm{YAl}}^2}{\mathrm{L}}\right)\times 2$

This energy, when imparted to the stone, it flies off a height 20 m.

Energy possessed by the stone = mgh. Now,

         $\begin{array}{l} \mathrm{U}=\mathrm{mgh}\Rightarrow \frac{{\mathrm{YAl}}^2}{\mathrm{L}}=\mathrm{mgh}\\ \mathrm{Y}=\frac{\mathrm{mghL}}{{\mathrm{Al}}^2}=\frac{1\times {10}^{-1}\times 10\times 25\times {10}^{-1}}{10\times {10}^{-6}\times {\left(5\times {10}^{-2}\right)}^2}\\ \therefore \mathrm{Y}=10\times {10}^8\mathrm{N}/{\mathrm{m}}^2\end{array}$