First slide

Law of conservation of momentum and it's applications

Question

A body is moving with a velocity v, breaks up into two equal parts. One of the part retraces back with velocity v. Then the velocity of the other part is

Moderate

A

v in forward direction
B

3v in forward direction
C

v in backward direction
D

3v in backward direction

Solution

Let the initial mass of body = m
Initial linear momentum = mv …(i)
When it breaks into equal masses then one of the fragment retrace back with same velocity
$∴$ Final linear momentum = $\frac{m}{2} (- v) + \frac{m}{2} (v_{2})$ …(ii)
By the conservation of linear momentum
$\Rightarrow mv = \frac{- mv}{2} + \frac{{mv}_{2}}{2} \Rightarrow v_{2} = 3 v$
i.e. other fragment moves with velocity 3v in forward direction

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