Momentum of a body is increased by 100 % . What is the percentage increase in its kinetic energy ?

Explanation

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