A light body and a heavy body have same linear momentum. Which one has a greater kinetic energy ?

Options

A. the heavy body
B. the light body
C. both have equal kinetic energy
D. data given is insufficient

Answer

B

Explanation

Momentum P=mv and `K.E. =1/2mv^(2)`
`therefore K=1/2 (m^(2)v^(2))/(m) =P^(2)/(2m)`
`therefore P^(2)=2Km therefore P=sqrt(2Km)`
Here both the bodies have the same K.E.
`therefore P alpha sqrt(m)`
Hence P is a large, if m is large. Thus the heavy body has a greater momentum.