Question

A stone of mass 'm' s projected from a rubber catapult of length 'l' and cross-sectional area A stretched by an amount 'e'. If Y be the young's modulus of rubber then the velocity of projection of stone?

• A. $Y\sqrt{\frac{A{e}^2}{lm}}$
• B. $\sqrt{\frac{A{e}^2}{lm}}$
• C. $Y\sqrt{\frac{YA{e}^2}{lm}}$
• D. $Y\sqrt{\frac{YA{e}^4}{lm}}$

Answer 1

The correct option is C $Y\sqrt{\frac{YA{e}^2}{lm}}$

Elastic energy stored in the rutter

$\begin{array}{c}U=\frac{1}{2}K{e}^2\text{where}K=\frac{YA}{L}\\ U=\frac{1}{2}\left(\frac{yA}{L}\right)\left(e^2\right)\end{array}$

Now, the energy stored is equal to the work done on mass 'm', which is equal to its change in Rinetic energy.$\Rightarrow$$\begin{array}{cc}\frac{1}{2}m{v}^2& =\frac{1}{2}\left(\frac{yA}{L}\right)\left(e^2\right)\\ v& =\sqrt{\frac{y_A{e}^2}{Lm}}\end{array}$