Question

A body of mass \( m \) moving with a constant velocity \( v \) hits another body of the same mass moving with the same velocity \( v \) but in the opposite direction and sticks to it. The velocity of the compound body after the collision is

• A. \( 2v \)
• B. \( \frac{v}{2} \)
• C. \( v \)
• D. zero

Hint:

In inelastic collisions where masses stick together, use momentum conservation. Opposite velocities of equal masses result in zero net momentum.

Answer 1

The Correct Option is D

This is a perfectly inelastic collision, where both bodies stick together after collision.
Using conservation of linear momentum: \[ \text{Initial momentum} = m \cdot v + m \cdot (-v) = mv - mv = 0 \] \[ \text{Final momentum} = (m + m)V = 2mV \Rightarrow 2mV = 0 \Rightarrow V = 0 \] So, the velocity of the compound body after the collision is zero.