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")`
The kinetic energy of a given body is doubled. Its momentum will

Options

A. remain unchanged
B. redoubled
C. become `(1)/(2)` times
D. become `sqrt(2)` times