Question

Question #71971

Answer 1

22.4%

Explanation:

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

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

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

Now the total Kinetic Energy is `K_2=K+1/2K=3/2K`
Now Momentum `p_2=sqrt(2mK_2)`
`p_2=sqrt(2m(3/2K))=sqrt(3/2(2mK))=sqrt(3/2) sqrt(2mK)`
But `sqrt(2mK)=p_1`
`p_2=sqrt(3/2)p_1=sqrt(3/2)p`

Increase in Momentum = `p_2-p_1=sqrt(3/2)p-p=(sqrt(1.5)-1)p`
`=0.224p`

Percent increase in momentum `=0.224p/pxx100%=22.4%`