JEE Main · 2021 · 24 Feb 2021 · Shift 1 · Conservation of Momentum

A ball with a speed of

9

m/s collides with another identical ball at rest. After the collision the direction of each ball makes an angle of

3 0^{\circ}

with the original direction. The ratio of velocities of the balls after collision is

x : y

, where

x

is ______.

Answer: 1

Solution

For elastic collision between identical balls where both move at

30°

to the original direction:

By momentum conservation along the original direction:

m v_{0} = m v_{1} cos 30° + m v_{2} cos 30°

9 = (v_{1} + v_{2}) \frac{3}{2}

By momentum conservation perpendicular to original direction:

0 = m v_{1} sin 30° - m v_{2} sin 30°

v_{1} = v_{2}

Substituting back:

9 = 2 v_{1} \times \frac{3}{2} = v_{1} 3

v_{1} = v_{2} = \frac{9}{3} = 33

The ratio is

v_{1} : v_{2} = 1 : 1

, so

x = 1

.

Answer: 1

JEE Main · 2021 · 24 Feb 2021 · Shift 1 · Integer answer