Question

A body is hanging from a rigid support by an inextensible string of length $l$. It is struck inelastically by an identical body of mass m moving with horizontal velocity $v=\sqrt{2gl}$, the tension in the string increases just after striking by :

• A. $mg$
• B. $3mg$
• C. $2mg$
• D. none of these

Answer 1

The correct option is C $2mg$

Let the velocity of the system after the collision be $v_1$ and tension in the string be $T_1$

Apply conservation of momentum before and after the collision :

$mv+0=\left(2m\right)v_1$

$m\times \sqrt{2gl}=\left(2m\right)v_1$ $⟹v_1=\sqrt{\frac{lg}{2}}$

Using circular motion equation, $\left(2m\right)\frac{v_1^2}{l}=T_1-2mg$

$\left(2m\right)\frac{lg}{2l}=T_1-2mg$ $⟹T_1=3mg$

Tension in the string initially $T=mg$

$\therefore$ Increase in tension $\Delta T=T_1-T$

$\Delta T=3mg-mg=2mg$