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Help me please, If the momentum of a ball is doubled, then the kinetic energy is

 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.
     

 
Answers (1)
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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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