# If the momentum of a ball is doubled, then the kinetic energy is   Option 1) 0.5 times larger.   Option 2) 2 times larger.   Option 3) 3 times larger.   Option 4) 4 times larger.

As learnt in

Perfectly Elastic Collision -

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

- wherein

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

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

$m_{1},m_{2}:masses$

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

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

$K.E. =P^2/2m$

$K.E.' =(2P)^2/2m\\$

$K.E.' =4P^2/2m$

If the momentum of a ball is doubled, then the kinetic energy is four times larger.

Option 1)

0.5 times larger.

This option is incorrect

Option 2)

2 times larger.

This option is incorrect

Option 3)

3 times larger.

This option is incorrect

Option 4)

4 times larger.

This option is correct

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