Two bodies of masses m and 4 m are moving with equal kinetic energies. The ratio of their linear momenta is

Question

Two bodies of masses m and 4 m are moving with equal kinetic energies. The ratio of their linear momenta is (A) 1: 2 (B) 1: 4 (C) 4: 1 (D) 1: 1

Tardigrade Admin · Accepted Answer

Mass of first body =m; Mass of second body =4 m and K1=K1. Linear momentum of a body p=√2 m E propto √m. Therefore (p1/p2)=√(m1/m2) =√(m/4 m)=√(1/4)=(1/2) or p1: p2=1: 2.

Q. Two bodies of masses $m$ and $4 m$ are moving with equal kinetic energies. The ratio of their linear momenta is

$1 : 2$

$1 : 4$

$4 : 1$

$1 : 1$

Mass of first body $= m$ ;
Mass of second body $= 4 m$ and $K_{1} = K_{1}$ .
Linear momentum of a body
$p = 2 m E \propto m$ .
Therefore $\frac{p _{1}}{p _{2}} = \frac{m _{1}}{m _{2}}$
$= \frac{m}{4 m} = \frac{1}{4} = \frac{1}{2}$
or $p_{1} : p_{2} = 1 : 2$ .

Q. Two bodies of masses m and 4m are moving with equal kinetic energies. The ratio of their linear momenta is

1:2

1:4

4:1

1:1