Question

The bodies of masses 2m and m have their kinetic energies in the ratio 8 : 1. Then the ratio of their momenta is :

• A. 1 : 1
• B. 2 : 1
• C. 4 : 1
• D. 8 : 1

Answer 1

The correct option is C 4 : 1

$KE=\frac{p^2}{2m}$
$\frac{K{E}_1}{K{E}_2}=\frac{p_1^2}{p_2^2}\times \frac{m_2}{m_1}$
$\frac{8}{1}=\frac{p_1^2}{p_2^2}\times \frac{m}{2m}$
$\frac{p_1}{p_2}=\sqrt{\frac{16}{1}}=\frac{4}{1}$