Question

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 30° with the original direction. The ratio of velocities of the balls after collision is x: y, where x is ______.

पर्याय

• 2

• 1

• 3

• 4

Answer 1

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 30° with the original direction. The ratio of velocities of the balls after collision is x: y, where x is 1.

Explanation:

As per question, the balls are identical, so, m₁ = m₂ = m

Initial speed of first ball u₁ = 9 m/s

Initial speed of second ball u₂ = 0

Applying the conservation of Linear Momentum

Momentum along y - axis

0 = mv₁ sin 30° - mv₂ sin 30°

V₁ = V₂ ⇒ V₁ : V₂ = 1 : 1

Momentum along x-axis

mu₁ + 0 = mv₁ cos 30° + mv₂ cos 30°

or 9 = v₁ × `sqrt3/2` + v₁ × `sqrt3/2`

or, V₁ = V₂ = 3`sqrt3`

⇒ V₁ : V₂ = 1 : 1

Hence, the ratio of velocities of ball after collision is x : y = 1 : 1, where x = 1.