Question

when momentum of a body increases by 100% then uts kinetic energy will increase by....

Answer 1

KE will increase by 300% as depicted in image.

Answer 2

Kinetic energy = p^2/2m    
If the momentum increases by 100% , then the p increases to 2p.

Substitute p =1
K before increase in momentum = p^2/2m = 1/2m                  - (1)
K' after increase in momentum by 100% = 2p^2/2m= 4/2m     - (2)

Let p = 1 
Divide (2) by (1) and substitute p=1
K'/K = (4/2m) / (1/2m)
            = 4 ( 2m gets divided by 2m to give 1)
      K'= 4K ( cross-multiplication)

Percentage increase = (K'-K / K) * 100
                                  = (4K-K/K) *100
                                  = (3K /K) *100
                                  = 3*100
                                  = 300%

When momentum of a body increases by 100% then its kinetic energy will increase by 300%.