Question

Two masses of $4gm$ and $1gm$ are moving with equal kinetic energies. The ratio of the magnitudes of their momenta is

• A. $4:1$
• B. $\sqrt{2}:1$
• C. $2:1$
• D. $1:16$

Answer 1

The correct option is C $2:1$

$K{E}_1=K{E}_2$ (Given)

$\frac{1}{2}{m}_1{v}_1^2=\frac{1}{2}{m}_2{v}_2^2$

$\frac{v_1^2}{v_2^2}=\frac{1}{4}$

$v_1=1$

$v_2=2$

Thus

$\frac{P_1}{P_2}=\frac{m_1{v}_1}{m_2{v}_2}$

$\frac{P_1}{P_2}=\frac{4\times 1}{1\times 2}$

$\frac{P_1}{P_2}=\frac{2}{1}$

So the ratio is 2:1