A solid cylinder of radius r and mass m is placed with no initial velocity on a moving belt 'B'. It is placed against a rough wall ’A', which restricts the sliding of the cylinder on the belt as shown in the figure. Assuming that the

coefficient of friction at A and B is `mu(lt 1)`, the angular acceleration of the cylinder will be

Options

A. `g/r (mu/(1 + mu))`
B. `(2g)/(r)((mu)/(1 + mu))`
C. `g/(2r) ((mu)/(1 + mu))`
D. `g/r ((mu)/(2 + mu))`

Answer

B

Explanation

For linear motion, apply newton.s laws
`N_1 - muN = 0 mu_1 = mu N " "......(i)`
`mu N_1 + mg = N .......(ii)`

For rotation motion.
`(mu N - mu N_1) • r = ((mr^2)/(2alpha))`
` (mu mg)/(1 - mu^2) - (mu^2 mg)/(1 - mu^2) = (mr)/2 alpha implies alpha = (2mug)/(r(1 + mu))`