NTA Abhyas JEE Main2020PhysicsElectrostaticsPractice
A nonconducting ring of mass m and radius R is charged as shown. The charged density i.e. charge per unit length is λ . It is then placed on a rough nonconducting horizontal surface plane. At time t = 0 , a uniform electric field E → = E 0 i ^ is switched on and the ring starts rolling without sliding. The friction force (magnitude and direction) acting on the ring, when it starts moving is
Options
- Aλ R E 0 i ^
- B3 λ R E 0 i ^
- C2 λ R E 0 i ^
- D2 λ R E 0 i ^
Correct answer
A. λ R E 0 i ^
Step-by-step solution
As E → will try to rotate the ring is clockwise direction friction will oppose the rotation and provide translational motion. so frictional force will act forward. dτ = (dq) × ( E 0 ) 2R sin θ dτ = (λ Rdθ) 2RE 0 sin θ τ = 2 R 2 λ E 0 ∫ 0 π / 2 sin  θ d θ = 2 R 2 λ E 0 ...(1) For translational motion,   f = m a ⇒ a   =   f m