Question

Two same masses are tied with equal lengths of strings and are suspended at the same point. One mass is suspended freely whereas another is kept in a way that string is horizontal as shown. This is given initial velocity u in vertical downward direction. It strikes the freely suspended mass elastically that is just able to complete the circular motion after the collision about point of suspension O. Magnitude of velocity u is :

• A. $\sqrt{gL}$
• B. $\sqrt{2.5gL}$
• C. $\sqrt{2gL}$
• D. $\sqrt{3gL}$

Answer 1

Answer: (D)

$\sqrt{3gL}$

Answer 2

As collision is elastic, freely suspended mass moves acquiring velocity of colliding mass after the collision. Also acquired velocity must be equal to $\sqrt{5gL}$ to complete the circular motion.

Hence, mgL = $\frac{1}{2}$ mu² = $\frac{1}{2}$ m(5gl)

u = $\sqrt{3gL}$ .