Question

Two bodies of masses $m$ and $4m$ are moving with equal kinetic energies. The ratio of their linear momenta is

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

Answer 1

The correct option is B $1:2$

We know that $P=mV$ and kinetic energy is $E=\frac{1}{2}m{V}^2$

using both we can get a formula $E=\frac{P^2}{2m}$ or $P=\sqrt{2mE}$

so the required ratio will be $\frac{P_1}{P_2}=\sqrt{\frac{m_1}{m_2}}=\sqrt{\frac{m}{4m}}$

so we get $P_1:P_2=1:2$