Relation between kinetic energy and momentum
Let us consider a body of mass 'm' having a velocity 'v', then
momentum of the body P = mass `xx` velocity
`P = m xx v rArr v = (P)/(m) " "...(1)`
From definition, kinetic energy (K.E) of the body
`K.E = (1)/(2) mv^(2)" "...(2)`
Now putting the value of (1) in (2) we have
`K.E = (1)/(2)m ((P)/(m))^(2)`
`K.E. = (1)/(2)m (P^(2))/(m^(2)) = (1)/(2) (P^(2))/(m) = (P^(2))/(2m)" "...(3)`
Thus we can write
`P^(2) = 2m xx K.E`
`rArr P = sqrt(2m xx K.E)`
Thus momentum = `sqrt(2 xx "mass" xx "kinetic energy")`
Two bodies masses 1 kg and 4 kg having equal kinetic energies. The ratio of their momentum is

Options

A. `4 : 1`
B. `1 : 4`
C. `2 : 1`
D. `1 : 2`