If momentum of an object is increased by 10%,then its kinetic energy will b increased by--?

using relation:

E=P ^{2}/2m

let p_{i}= initial momentum

then according to question,final momentum p_{f}=10% of p_{i}+p_{i}

=11p_{i}/10

initial kinetic energy E_{i}=P_{i}^{2}/2m

final kinetic energy E_{f}=P_{f}^{2}/2m=(11p_{i}/10)^{2}/2m

=121p_{i}^{2}/200m

so change in kinetic energy = E_{f} – E_{i}

_{ }= (121P_{i}^{2}/200m) - (P_{i}^{2} /2m)

= 21P_{i}^{2}/200m

= 21/200(P_{i}^{2}/2m)

= 21% of E_{i}

so, the kinetic energy increases by 21% when momentum increases by 10%

@Anushree....Very nicely done, thanks for the help!

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