Question

if the momentum of a body increases by 50percent then its kinetic energy will increase by how much?
$77$

Answer 1

Hello here is your answer by Sujeet yaduvanshi



ANS:-


GIVEN:-
Momentum of a body increase by 50%
then,
Kinetic energy will be
Kinetic Energy = 1/2 * m * v * v

mv = Momentum

If momentum is increased by 50% then Momentum is 3mv / 2

Kinetic Energy now = 1/2 * 3mv / 2 * v = 3mv2/ 4

Percentage increase in kinetic energy = ( 3mv2 / 4 - 1mv2 / 2 ) / (1mv2 / 2) * 100

= ( mv2 / 4 ) / ( (1mv2 / 2) * 100

= 1/2 * 100

= 50%

Ans: 50%

Answer 2

Relation between kinetic energy(KE) and momentum(p) of an object of mass m is given as

KE = p^2 / 2m

If momentum is increased by 50%,
50% of p = p × 50/100 = 0.5p
New momentum, p' = p + 0.5p = 1.5p

New kinetic energy, KE' = p'^2 / 2m

KE' = (1.5p)^2 / 2m

KE' = 2.25p^2 / 2m = 2.25 KE

Increase in Kinetic energy = KE' - KE = 2.25KE - KE = 1.25 KE

% Increase = 1.25KE/KE × 100 = 125%

Thus, Kinetic energy will increase by 125% by 50% increase in momentum.