if momentum of a body increases by 20 percent, then percentage increase in its kinetic energy is...
We know,
KE = ½ mv2
P = mv
Therefore, KE = ½ (mv)2/m = p2/(2m)
Considering the mass to be constant, if the momentum is increased by 20%, let the new momentum be,
P/ = P + 0.2P = 1.2P
The new kinetic energy is, KE/ = (P/)2/(2m)
=> KE/ = (1.12)[P2/(2m)] = 1.44KE
=> (KE/)/KE = 1.44
=> (KE/ - KE)/KE = 0.44
=> (KE/ - KE)/KE × 100% = 44%