The relationship between the kinetic energy and momentum of a body is K.E=P2/2m.
Given that, if momentum is increased by 10%, then by what % the K.E will increase. So, the initial momentum be P and initial kinetic energy be K.E=P2/2m.
Increase in momentum = 10% of P, i.e.
⇒10/100×P =P/10 So, final momentum = initial momentum + increased momentum.
Final momentum, P1 = P + P/10 =11P/10. Then, final kinetic energy,
⇒K.E1 = (P1)2/2m
We have final momentum = 11P/10, putting this value,
we get ⇒K.E1=(11P/10)2/2m = 121P2/2m×100
⇒K.E1=121/100 × P2/2m = 121/100 K.E.
Now, increase in kinetic energy = final kinetic energy – initial kinetic energy. increase in kinetic energy =121/100K.E − K.E
increase in kinetic energy =121K.E−100K.E/100
increase in kinetic energy =21K.E/100
% increase in kinetic energy. ⇒21%
Hence, we can see that if the momentum of an object increases by 10%, then the kinetic energy will increase by 21%.