Figure shows a ball having a charge q fixed at a point A. Two identical balls of mass m having charge +q and –q are attached to the end of a light rod of length 2a. The system is released from the situation shown in figure. Find the angular velocity of the rod when the rod turns through 90º.

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

$\frac{q}{\sqrt{6 {πε}_{0} {ma}^{3}}}$

$\frac{\sqrt{2} q}{3 {πε}_{0} {ma}^{3}}$

$\frac{q}{\sqrt{3 {πε}_{0} {ma}^{3}}}$

$\frac{\sqrt{2} q}{4 {πε}_{0} {ma}^{3}}$

answer is C.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Initial potential energy = 0

Final potential energy = $\frac{- {kq}^{2}}{a} + \frac{{kq}^{2}}{3 a} = \frac{- 2 {kq}^{2}}{3 a}$

As the total mechanical energy is conserved.

$ΔU + ΔKE = 0$

$\Rightarrow \frac{1}{2} (2 {ma}^{2}) ω^{2} = \frac{2 {kq}^{2}}{3 a}$

$ω = \sqrt{\frac{2 {kq}^{2}}{3 {ma}^{3}}} = \sqrt{\frac{q}{6 {πε}_{0} {ma}^{3}}}$

Watch 3-min video & get full concept clarity