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Two bodies of masses m and 4 m are movin...

Two bodies of masses m and 4 m are moving with equal K.E. The ratio of their linear momentums is

A

1: 4

B

1 : 2

C

1 : 1

D

2 : 1

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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

SL ARORA-Work, Energy and power-EXERCISE
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