When the KE of body is increased by 100% the momentum of the body is increased by?

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When the KE of body is increased by 100% the momentum of the body is increased by?

Text Solution

Solution : Let the mass of the body be m . <br> Initial momentum = `p_1` , hence , final momentum after a 100 % increase, `p_2=2p_1`. <br> If `K_1 and K_2` are initial and final kinetic energies, <br> `K_1=(p_1^2)/(2m) and K_2 =(p_2^2)/(2m)` <br> `therefore (K_2)/(K_1)=(p_2^2)/(p_1^2)=((2p_1)^2)/(p_1^2) =4 =4/1` <br> `or, (K_2-K_1)/(K_1)xx100=(4-1)/1xx100=300` <br> So, the kinetic energy increases by 300% .

1) 150%

2) 200%

3) 225%

4) 300%

Answer: 4) 300%

Solution:

Kinetic Energy (K.E) = p2/2m ( p = momentum, m = mass)

Momentum is increased by 100% then,

Kinetic Energy (K.E) = (2p)2/2m

= 4p2/2m

The percentage increase in kinetic energy

= [4p2/2m – p2/2m]/p2/2m

= 300 %

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