Question

The ratio of kinetic energies of two bodies is $2:1$ and their momenta are in the ratio $1:2$, the ratio of their masses is

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

Answer 1

The correct option is D $1:8$

$\frac{K.E_1}{K.E_2}=\frac{\frac{1}{2}{m}_1{v}_1^2}{\frac{1}{2}{m}_2{v}_2^2}$

$\frac{2}{1}=\frac{m_2}{m_1}\times \frac{m_1{v}_1^2}{m_2{v}_2^2}=\frac{m_2}{m_1}(\frac{1}{2}{)}^2$

$\frac{m_1}{m_2}=1:8$