A ball of mass 10 kg is moving with a velocity of 10 m/s. It strikes another ball of mass 5 kg, which is moving in the same direction with a velocity of 4 m/s. If the collision is elastic, then their velocities after collision will be respectively

Question

A ball of mass 10 kg is moving with a velocity of 10 m/s. It strikes another ball of mass 5 kg, which is moving in the same direction with a velocity of 4 m/s. If the collision is elastic, then their velocities after collision will be respectively (A) 12 m/s, 6 m/s (B) 12 m/s, 25 m/s (C) 6 m/s, 12 m/s (D) 8 m/s, 20 m/s

Tardigrade Admin · Accepted Answer

Since, collision is elastic momentum remains conserved, hence we have Momentum before collision = Momentum after collision Initially,

p = m_{1} u_{1} + m_{2} u_{2} = 10 \times 10 + 5 \times 4 = 120

..(i)
Final,

p = m_{1} v_{1} + m_{2} v_{2} = 10 v_{1} + 5 v_{2}

..(ii)
Equating Eqs. (i) and (ii), we get

10 v_{1} + 5 v_{2} = 120

\Rightarrow

2 v_{1} + v_{2} = 24

..(iii)
Since collision is elastic relative velocity remains unchanged in magnitude but is reversed in direction,

e = 1 = \frac{v _{2} - v _{1}}{u _{1} - u _{2}}

\Rightarrow

10 - 4 = v_{2} - v_{1}

..(iv)

∴

v_{2} - v_{1} = 6

Solving Eqs. (iii) and (iv), we get

v_{1} = 6 m / s, v_{2} = 12 m / s

Q. A ball of mass 10 kg is moving with a velocity of 10 m/s. It strikes another ball of mass 5 kg, which is moving in the same direction with a velocity of 4 m/s. If the collision is elastic, then their velocities after collision will be respectively

12 m/s, 6 m/s

12 m/s, 25 m/s

6 m/s, 12 m/s

8 m/s, 20 m/s