Question

A particle having mass m and positive charge q whirls along vertical circle of radius R. At the centre of circle, another positive charge $2q$ is fixed.

• A. The minimum velocity given at the lowest point to complete vertical circular motion is less than .$\sqrt{5gR}$ for motion in gravity.
• B. For any value of velocity given in horizontal direction at the lowest point in gravity free space it will perform vertical circular motion.
• C. Tension in gravity free space cannot becomes zero at any point during motion.
• D. If the charge at the centre is removed and considering the motion in gravity tension will also be function of charge on particle.

Answer 1

Answer: (A), (B), (C)

The minimum velocity given at the lowest point to complete vertical circular motion is less than .$\sqrt{5gR}$ for motion in gravity.
For any value of velocity given in horizontal direction at the lowest point in gravity free space it will perform vertical circular motion.
Tension in gravity free space cannot becomes zero at any point during motion.

Balancing forces at the end point of the circle.

$mg-2\frac{k{q}^2}{r^2}+T=\frac{m{v}^2}{r}$

$-mgR+\frac{1}{2}m{u}^2=mgR+\frac{1}{2}m{v}^2$

if T = 0 then $u_{mh}=\sqrt{5gR-\frac{2k{q}^2}{mR}}$