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Question

A shell of mass m moving with velocity V suddenly breaks into 2 pieces. The part having mass m4 remains stationary. The velocity of the other shell will be:


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Solution

Step 1: Given data

  1. The mass of the body is m
  2. The mass of the two broken parts after the explosion is m4 and m-m4.
  3. The velocity of the body is V.
  4. The velocity of the first piece of mass m4 is v1=0.

Step 2: Formula used

  1. The linear momentum of a body is the product of the mass and velocity of the body, i.e, linear momentum, P=mv, where, m and v are the mass and velocity of a body.
  2. We know in an explosion the linear momentum is conserved. So, MV=m1v1+m2v2, where, M and V are the mass of the body, m1,m2 and v1,v2 are the masses and velocities of the broken pieces.

Step 3: Finding the velocity of the second piece

Let, v2 be the velocity of the second piece.

According to the conservation of linear momentum, MV=m1v1+m2v2

So,

mv=m4×0+m-m4v2Since,v1=0.ormv=3m4×v2orv2=4mv3m=43vorv2=43v.

Therefore, the velocity of the second piece is 43v.


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