Question

Two bodies of masses m and 4 m are moving with equal kinetic energy. Then the ratio of their linear momentum will be:

• A. 1 ; 1
• B. 2 : 1
• C. 4 : 1
• D. 1 : 2

Answer 1

The correct option is D 1 : 2

Relation between momentum and energyis
$E=\frac{p^2}{2m};E=\frac{p_1^2}{2m};E=\frac{p_2^2}{2\times 4m}$
$\frac{p_1^2}{2m}\times \frac{2\times 4m}{p_2^2}=\frac{E}{E}=1$
$\frac{p_1^2}{p_2^2}=\frac{1}{4}\Rightarrow \frac{p_1}{p_2}=\frac{1}{2}\Rightarrow p_1:p_2=1:2$