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Question

A body of mass 300 g kept at rest breaks into two parts due to internal force,One part of mass 200 g is found to move at a speed of 12 m/s towards the east. What will be the velocity of the other part ?

A
12 m/s, Westwards
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B
12 m/s, Eastwards
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C
24 m/s, Westwards
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D
23 m/s, Eastwards
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Solution

The correct option is C 24 m/s, Westwards

Before it broke, the body was at rest.The linear momentum of the body was thus p=mv=0.
The body breaks due to internal forces. As the external force acting on it is zero,its linear momentum will remain constant, i.e.,zero.

The linear momentum of the first part is
P1=m1v1=(200g)×(12 m/s), towards the east.
For the total momentum to remain zero, the linear momentum of the other part must have the same magnitude and should be opposite in direction. It therefore moves towards the west. If its speed is v2, its linear momentum is
P2=m2v2=(100g)×v2
Thus,
(200g)×(12 m/s)=(100g)×v2
v2=24 m/s
The velocity of the other part is 24 m/s towards the west.

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