A heavy body and a light body have equal K.E. which one of them has hreater momentum?

Options

A. Light body
B. Heavy body
C. Both have equal momentum
D. A body with higher velocity

Answer

B

Explanation

Let M and m be the masses of the heavy and light bodies
respectively. K.E. of the body `=(1)/(2)Mv^(2)`
Momentum of the heavy body
`=Mv=sqrt(M^(2)v^(2))=sqrt((1)/(2)Mv^(2)xx2M)=sqrt(2EM)`
`thereforeP_(H)=sqrt(2EM)`
Similarly the momentum of the light body
`=sqrt(2Em)=P_(L)`
As both of them have the same `"K.E. "therefore P_(H) gt P_(L)`
`therefore" The heavy body has a larger momentum."`