Two bodies of masses m and 2m have equal kinetic energies. The ratio of their linear momenta is

Question

Two bodies of masses m and 2m have equal kinetic energies. The ratio of their linear momenta is (A)  1  (B)  (1/2)  (C)  (1/√2)  (D) 2

Tardigrade Admin · Accepted Answer

Kinetic energy is the energy possessed by a body due to its velocity.

K = \frac{1}{2} m v^{2} \dots

(i)
Momentum

(p) =

mass

(m) \times

velocity

(v) \dots

(ii)
From Eqs. (i) and (ii), we get

p = 2 m K

Given,

m_{1} = m

, and

m_{2} = 2 m

∴ \frac{p _{1}}{p _{2}} = \frac{1}{2}

Q. Two bodies of masses $m$ and $2 m$ have equal kinetic energies. The ratio of their linear momenta is