First slide

The steps in collision

Question

A particle A of mass m initially at rest slides down a height of 1.25 m on a frictionless ramp, collides with and sticks to an identical particle B of mass m at rest as shown in the figure.
Then, particles A and B together collide elastically with particle C of mass 2m at rest. The speed of particle C after the collision with combined body (A + B) would be (Take, $g = 10 {ms}^{- 2}$ )

Moderate

A

$2 {ms}^{- 1}$
B

$1.25 {ms}^{- 1}$
C

$2.5 {ms}^{- 1}$
D

$5 {ms}^{- 1}$

Solution

Velocity of A just before collision
$= \sqrt{2 g h} = \sqrt{2 \times 10 \times 1.25} = 5 {ms}^{- 1}$
Velocity of (A + B) just after collision $= \frac{5}{2} = 2.5 {ms}^{- 1}$
In elastic collision between two bodies of equal masses, velocities are interchanged.
Hence, velocity of C will become $2.5 {ms}^{- 1}$

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