Question

The ratio of kinetic energies of two bodies is $2:1$ and their momentum are in the ratio of $1:2$. The ratio of their masses will be:

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

Answer 1

Answer: (D)

$1:8$

$K.E=\frac{1}{2}\frac{p^2}{2m}$ where p=momentum

$\frac{\frac{1}{2}{p^2}_1/m_1}{\frac{1}{2}{p^2}_2/m_2}={\left(\frac{p_1}{p_2}\right)}^2\left(\frac{m_2}{m_1}\right)\frac{2}{1}={\left(\frac{1}{2}\right)}^2\left(\frac{m_2}{m_1}\right)\frac{m_1}{m_2}=1:8$