Question

A particle of mass $m$ moves with constant speed $v$ on a circular path of radius $r$ as shown in figure. The average force on it during its motion from $A$ to $B$ is

• A. $\frac{\sqrt{3} m v^{2}}{2 \pi r}$
• B. $\frac{m v^{2}}{r}$
• C. $\frac{2 \sqrt{3} m v^{2}}{\pi r}$
• D. $\frac{3 \sqrt{3} m v^{2}}{4 \pi r}$

Answer 1

Answer: (D)

$F =m a=\frac{m \Delta v}{\Delta t}=\left[\frac{2 v^{2} \sin \theta / 2}{r \theta}\right]$
$=m\left[\frac{2 v^{2} \sin (2 \pi-2 \pi / 3)}{r \cdot\left(\frac{4 \pi}{3}\right)}\right]$
$=\frac{3 \sqrt{3} m v^{2}}{4 \pi r}$