Question

If two bodies of masses m and 2m have same momentum, what will be the ratio of their kinetic energy?

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

Answer 1

The correct option is C $1:\sqrt{2}$

$E=\frac{P^2}{2m}$
If momentum is same then $E\propto \frac{1}{m}$
$k=\frac{1}{2}m{v}^2,m{v}^2=2k$
$p^2=m\left(2k\right)$
$k=\frac{P^2}{\left(2m\right)}$
Since their kinetic energies are equal
$\frac{p_1^2}{2m_1}=\frac{p_2^2}{2m_2}$
$\frac{p_1}{p_2}=\sqrt{\frac{m_1}{m_2}}=\sqrt{\frac{m}{2m}}$
$\frac{p_1}{p_2}=\sqrt{\frac{1}{2}}$