A body of mass M moving with a velocity V explodes into two equal parts. If one comes to rest and the other body moves with velocity v, what would be the value of v?a)Vb)V/√2c)4Vd)2VCorrect answer is option 'D'. Can you explain this answer?

Question

A body of mass M moving with a velocity V explodes into two equal parts. If one comes to rest and the other body moves with velocity v, what would be the value of v?a)Vb)V/&radic;2c)4Vd)2VCorrect answer is option 'D'. Can you explain this answer?

Answer

By conservation of momentum, the total momentum before the explosion is equal to the total momentum after the explosion.

Before the explosion: momentum = MV

After the explosion: momentum = (1/2)(M)(0) + (1/2)(M)(v) = (1/2)(M)(v)

Setting the two equal, we have:

MV = (1/2)(M)(v)

Dividing both sides by M, we get:

V = (1/2)v

Multiplying both sides by 2, we get:

2V = v

Therefore, the value of v is 2V.

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