Question

A particle of mass ${}^{\prime }{m}^{\prime }$ describes a circle of radius $\left(r\right)$. The centripetal acceleration of the particle is $\frac{4}{r^2}$. The momentum of the particle:

• A. $\frac{2m}{r}$
• B. $\frac{2m}{\sqrt{r}}$
• C. $\frac{4m}{r}$
• D. $\frac{4m}{\sqrt{r}}$

Answer 1

The correct option is B $\frac{2m}{\sqrt{r}}$

Centripetal acceleration of the particle, $a=\frac{v^2}{r}$

$\therefore$ $\frac{4}{r^2}=\frac{v^2}{r}$ $⟹v=\frac{2}{\sqrt{r}}$

Thus the momentum of the particle, $P=mv=\frac{2m}{\sqrt{r}}$