The momentum of a body is increased by 25%. The kinetic energy is increased by about :

Options

A. `25%`
B. `5%`
C. `56%`
D. `38%`

Answer

C

Explanation

The relation between K and p is
`" "p=sqrt(2K)m`
When increased by 25%, we have
`" "p.=p+25/100p=(5p)/4`
`rArr" "(4p)/(50)=K_(1)/K_(2)`
`rArr" "K_(1)/K_(2)=16/25`
Hence, percentage increase is
`" "=(25-16)/16 times 100=9/16 times 100=56.25%`