Question

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

• A. $4:1$
• B. $\sqrt{2}:1$
• C. $1:2$
• D. $1:6$

Answer 1

The correct option is C $1:2$

The kinetic energy is given as
$K.E=\frac{P^2}{2m}$
For the two masses we have:
$K.E_1=\frac{P_1^2}{2m_1};K.E_2=\frac{P_2^2}{2m_2}\text{As, Both the masses are moving with}\text{equal K.E.}\Rightarrow K.E_1=K.E_2\frac{P_1^2}{2m_1}=\frac{P_2^2}{2m_2}{\left(\frac{P_1}{P_2}\right)}^2=\frac{m_1}{m_2}\frac{P_1}{P_2}=\sqrt{\frac{m_1}{m_2}}\frac{P_1}{P_2}=\sqrt{\frac{m_1}{m_2}}=\sqrt{\frac{1}{4}}=\frac{1}{2}$