COMEDK202510 May 2025Evening ShiftPhysicsElectrostaticsActual
A particle ' X ' carrying a charge +Q is moving in a circular path of radius R around another particle ' Y ' having a charge -Q with a frequency ' v '. Then the mass ' m ' of the charged particle is
Options
- AM= Q^2 [16 ^3 ₀ R^2 v^2 ]
- BM= Q^2 [16 ^2 ₀ R v^2 ]
- CM= Q^2 [16 ^2 ₀ R^3 v^2 ]
- DM= Q^2 [16 ^3 ₀ R^3 v^2 ]
Correct answer
D. M= Q^2 [16 ^3 ₀ R^3 v^2 ]
Step-by-step solution
The electrostatic force between the two charges Q and -Q separated by a distance R provides the necessary centripetal force for the circular motion of particle X . The electrostatic force is given by Coulomb's law as F_ e = 1 4 ₀ Q^2 R^2 . The centripetal force required for circular motion is F_ c = m ^2 R , where is the angular frequency. Given the frequency v , the angular frequency is = 2 v . Equating the forces: 1 4 ₀ Q^2 R^2 = m (2 v)^2 R . Simplifying the equation: Q^2 4 ₀ R^2 = m (4 ^2 v^2) R . Solving for m