Question #71971

1 Answer
Sep 27, 2017

22.4%

Explanation:

The relation between kinetic energy KK and momentum pp of an object is
p=sqrt(2mK)p=2mK
where m is the mass of object

First let momentum is p_1=p=sqrt(2mK)p1=p=2mK
and Kinetic Energy K_1=KK1=K

Now Kinetic Energy of Body is increased by 50%.
Increase in Kinetic energy =Kxx50/100=K/2=K×50100=K2

Now the total Kinetic Energy is K_2=K+1/2K=3/2KK2=K+12K=32K
Now Momentum p_2=sqrt(2mK_2)p2=2mK2
p_2=sqrt(2m(3/2K))=sqrt(3/2(2mK))=sqrt(3/2) sqrt(2mK)p2=2m(32K)=32(2mK)=322mK
But sqrt(2mK)=p_12mK=p1
p_2=sqrt(3/2)p_1=sqrt(3/2)pp2=32p1=32p

Increase in Momentum = p_2-p_1=sqrt(3/2)p-p=(sqrt(1.5)-1)pp2p1=32pp=(1.51)p
=0.224p=0.224p

Percent increase in momentum =0.224p/pxx100%=22.4%=0.224pp×100%=22.4%