if momentum of a body increases by 20 percent, then percentage increase in its kinetic energy is...

We know,

KE = ½ mv^{2}

P = mv

Therefore, KE = ½ (mv)^{2}/m = p^{2}/(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^{/} = (1.1^{2})[P^{2}/(2m)] = 1.44KE

=> (KE^{/})/KE = 1.44

=> (KE^{/} - KE)/KE = 0.44

=> (KE^{/} - KE)/KE × 100% = 44%

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