A bomb of mass  16 kg  at rest  explodes into  two  pieces of  masses  of 4  Kg and 12 Kg  .  The  velocity of  the 12  Kg  mass is 4 ms-1 . The kinetic energy of the other mass is 

Option 1)

96 J

Option 2)

144 J

Option 3)

288 J

Option 4)

192 J.

Answers (1)

As we learnt in

Perfectly Elastic Collision -

Law of conservation of momentum and that of Kinetic Energy hold good.

- wherein

\frac{1}{2}m_{1}u_{1}^{2}+\frac{1}{2}m_{2}u_{2}^{2}= \frac{1}{2}m_{1}v_{1}^{2}+\frac{1}{2}m_{2}v_{2}^{2}

m_{1}u_{1}+m_{2}u_{2}=m_{1}v_{1}+m_{2}v_{2}

m_{1},m_{2}:masses

u_{1},v_{1}:initial \: and\: final \: velocity\: of \: the\: mass\ m_{1}

u_{2},v_{2}:initial \: and\: final \: velocity\: of \: the\: mass\ m_{2}

 

 From conservation of linear momentum

    pi = pf

    0=4\times 12+4\times v

Therefore v = -12 m/s

i.e. 4 kg mass will move with 12 m/s in opposite direction.

Kinetic energy of 4 kg mass =\frac{1}{2}\times 4\times(12)^{2}=288J

Correct answer is 3


Option 1)

96 J

This is an incorrect option.

Option 2)

144 J

This is an incorrect option.

Option 3)

288 J

This is the correct option.

Option 4)

192 J.

This is an incorrect option.

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