Question

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

• A. 4 : 1
• B. 2 : 1
• C. 1 : 2
• D. 1 : 16

Answer 1

The correct option is C 1 : 2

Kinetic energy $K=\frac{p^2}{2m}$

Two masses are given as- $m_1=1gm$ and $m_2=4gm$

But $K_1=K_2$

$\therefore$ $\frac{p_1^2}{2m_1}=\frac{P_2^2}{2m_2}$

Or $\frac{P_1^2}{2\left(1\right)}=\frac{P_2^2}{2\left(4\right)}$

$⟹$ $P_1:P_2=1:2$