Question

Two bodies $A$ and $B$ having mass $M$ and $m$ respectively possesses same kinetic energy. Given that $M>m$. If ${\rho }_A$ and ${\rho }_B$ be their momentum, then which of the following statements is true?

• A. ${\rho }_A={\rho }_B$
• B. ${\rho }_A>{\rho }_B$
• C. ${\rho }_A<{\rho }_B$
• D. It cannot be predicted

Answer 1

Answer: (C)

${\rho }_A<{\rho }_B$

Two bodies A and B having mass m and M respectively possesses same Kinetic energy :

$K_A=K_B$

In general kinetic energy, $K=\frac{1}{2}m{v}^2=\frac{p^2}{2m}$ where $p$ is momentum.

$\therefore \frac{{\rho }_A^2}{2M}=\frac{{\rho }_B^2}{2m}$

$\frac{{\rho }_A^2}{M}=\frac{{\rho }_B^2}{m}$

But $M>m$ and therefore for above equation to be true ${\rho }_A^2<{\rho }_B^2$ or ${\rho }_A<{\rho }_B$