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Question

If a bomb at rest explodes and splits into two equal fragments, the fragments will move in

A
one direction and with equal velocities.
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B
opposite directions with different velocities.
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C
one direction with different velocities.
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D
opposite directions with equal velocities.
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Solution

The correct option is D opposite directions with equal velocities.
Let the mass of the bomb be M.
The masses of two equal fragments of the bomb is M2 each.
Let U be the initial velocity of the bomb and v1 and v2 be the velocity of the fragments after explosion.
As there is no external force applied in this case,
momentum before explosion = momentum after explosion.
i.e, MU=M2 v1+M2 v2
As bomb was at rest initially, MU=0
we have, M2 v1+M2 v2 will also be equal to zero.
M2 v1+M2 v2=0
M2 v1=M2 v2
v1=v2
This means the fragments will move in opposite directions with equal velocity.

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