Question

A ball moving with velocity 5 m/s collides head on with another stationary ball of double mass. If the coefficient of restitution is 0.8, then their velocities (in m/s) after collision will be ____________.

Options

• 0, 1

• -1, 3

• -1, 5

• 0, 5

Answer 1

A ball moving with velocity 5 m/s collides head on with another stationary ball of double mass. If the coefficient of restitution is 0.8, then their velocities (in m/s) after collision will be -1, 3.

Explanation:

Let v₁ and v₂ be their respective velocities after collision

Applying the Jaw of conservation of linear momentum,

m₁u₁ + m₂u₂ = m₁v₁ +m₂v₂

∴ m x 5 + 2m x 0 = m₁ x v₁ + 2m x v₂

5m=mv₁ +2mv₂

5 = (v₁ + 2v₂)       .....(i)

By definition of coefficient of restitution,

e = `("v"_2 - "v"_1)/( "u"_1 - "u"_2)`

e(u₁ - u₂) = v₂ - v₁

0.8(5 - 0) = v₂ - v₁   ......(ii)

4 = v₂ - v₁

Solving equations (i) and (ii),

v₁ = -1 m/s, v₂ = 3 m/s