One end of an insulating rigid rod of negligible mass and length $l$ is pivoted to a fixed point O: A small ball of mass m having a negative charge of magnitude q is attached to the lower end of the rod. Another small ball carrying a positive charge Q is fixed at a height h above the point O as shown in the figure. What should the range of values of mass $m$ of the lower ball be so that the rod remains in a state of stable equilibrium? Acceleration due to gravity is g.

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

$m > \frac{Q q h}{4 π ε_{0} g {(h + l)}^{3}}$

$m > \frac{Q q}{4 π ε_{0} g {(h + l)}^{2}}$

$m < \frac{Q q h}{8 π ε_{0} g {(h + l)}^{3}}$

$m < \frac{Q q h}{4 π ε_{0} g {(h + l)}^{3}}$

answer is C.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

For stable equilibrium
$\frac{\sin β}{l} = \frac{\sin (α - β)}{h} h = (\frac{l \sin (α - β)}{\sin β}) \frac{β}{l} = \frac{(α - β)}{h} h β = α l - β l β = (\frac{α l}{h + l}) M g l \sin α > \frac{K Q q}{{(h + l)}^{2}} \frac{(h) α l}{(h + l)} m > \frac{Q q h}{4 π ε_{0} g {(h + l)}^{3}}$

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

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

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE