If momentum of a body increase by 25% its kinetic energy will increase by

Options

A. 25%
B. 5%
C. `125%`
D. 56%

Answer

D

Explanation

Let momentum of `p_(1)=100%"momentum of " p-(2)=125%`.
`p_(2)/p_(1)=5/4impliesp^(2)5/4p_(1) therefore v_(2)=5/4v_(1)`
`"kinetic energy"=1/2mv(2)`
`Einftyv^(2) E_(2)=(25)/(16)E_(1)`
`"Increase in" K.E.=(E_(2)-e_(1))/e_(1)xx100=((25)/(16)E_(1)-E_(1))/E_(1)xx100`
`=((25-16)/16E_(1))/E_(1)xx100=9/(16)xx100=56.25%`