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

Kinetic energy of a body is , `K = (p^2)/(2m)`
where p is the momentum and m is the mass of the body.
`:. K prop p^2`
when the momentum of a body is increased by 25% , its mometum will become
`p. = p + 25/100 p = 125/100 p = 5/4 p`
`:. (K.)/(K) = (p.^2)/(p^2) = (5/4)^2 = 25/16 or K. = 25/16 K`
Percentage increase in the kinetic energy of the body
`= (K. - K)/(K) xx 100 % = ((25//16) K-K)/(K) xx 100%`
`= 9/16 xx 100% = 56%`.