Two balls having masses m and 2m are fastened to two light strings of same length shown in the figure. The other ends of the strings are fixed at O. The strings are kept in the same horizontal line and the system is released from rest. The collision between the balls is elastic. (a). Find velocities of the balls just after their collision. (b). How high will the balls rise after the collision.

Options

A. a.`2(sqrt(2gl))/(3)`
B. b.`2(sqrt(50 gl))/(3)`
C. c.`(sqrt(2gl))/(3)`
D. d.`(sqrt(50 gl))/(3)`

Answer

C

Explanation

The speed of both balls just before collision is `u = sqrt(2gl)`.
From conservation of momentum
`m u - 2m u = mv_(1) + 2mv_(2)` …(i)
From equation of coefficient of restituation `e = 1 = (v_(2) - v_(1))/(2 u)` …(ii)
Solving equation (i) and (ii) `v_(1) = (u)/(3) = (sqrt2gl)/(3)`