Question

A particle of mass $m$ moves along a circle of radius $R$. Find the modulus of the average vector of the force acting on the particle over the distance equal to a quarter of the circle, if the particle moves uniformly with velocity $v$.

• A. $2\sqrt{2}\frac{m{v}^2}{\pi R}$
• B. $\frac{m{v}^2}{\sqrt{2}\pi R}$
• C. $2\frac{m{v}^2}{\pi R}$
• D. $\sqrt{2}\frac{m{v}^2}{\pi R}$

Answer 1

The correct option is A $2\sqrt{2}\frac{m{v}^2}{\pi R}$

Average vector of the force over a distance of quarter of the circle is given by rate of change in momentum between the initial and the final point .
$\overrightarrow{F_{avg}}=\frac{P_2-P_1}{t}$

$=\frac{\sqrt{2}mv(\hat{i}-\hat{j})}{\frac{\pi R}{2v}}$

$|\overrightarrow{F_{avg}}|=\frac{2\sqrt{2}m{v}^2}{\pi R}$