Two bodies A and B of same mass undergo completely inelastic one dimensional collision. The body A moves with velocity while body B is at rest before collision. The velocity of the system after collision is . The ratio is [2024]

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Solution

Q.
Two bodies A and B of same mass undergo completely inelastic one dimensional collision. The body A moves with velocity $v_{1}$ while body B is at rest before collision. The velocity of the system after collision is $v_{2}$ . The ratio $v_{1} : v_{2}$ is [2024]

1 1 : 2

2 2 : 1

3 4 : 1

4 1 : 4

Ans.
(2)

Given, $m_{A} = m_{B} = m,$ $u_{A} = v_{1},$ $u_{B} = 0$

In completely inelastic collision when two bodies have same mass and one is at rest, then after collision they stick together and move with common velocity $v_{2}$ .

By conservation of momentum,

$m_{A} u_{A} + m_{B} u_{B} = (m_{A} + m_{B}) v_{2}$

$m v_{1} + 0 = 2 m v_{2}$

$∴$ $\frac{v_{1}}{v_{2}} = 2$

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