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

Question

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, λ R E 0 i ^, 3 λ R E 0 i ^, 2 λ R E 0 i ^, 2 λ R E 0 i ^

MARKS App · Accepted Answer

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 . . . ( 2 ) For rotational motion , τ - f R = ( m R 2 ) ( a R ) ...(3) From (2) and (3) τ = 2 f r R ...(4) From (1) and (4) f r = τ 2 R = 2 R 2 λ E 0 2 R = R λ E 0 ⇒ f → r = R λ E 0 i ^

Search any question & find its solution

Looking for more such questions to practice?