Question

The kinetic energy of a body increased by 25 percent. How it's linear momentum change.

Answer 1

The relation between kinetic energy, K and momentum p is the following
K=p^2/2.....................(1)
Since, the is the same, mass remains constant.
If momentum increases by 25% then the new momentum will be
p’=1.25 p . Hence, the new kinetic energy will be K’= (1.25)^2p^2/2m....................(2)
Then, (K’-K)/K = [p^2/2m(1.25)^2-1]/(p^2/2m) = [(1.25)^2-1] = 1.56-1. = 0.56
Therefore % increase in kinetic energy = 0.56x100 = 56%