Question

A disc is standing on a flat rough surface. Its centre is suddenly given a velocity of 5m/s in the forward direction. In how much time will pure rolling start? Mass = 1kg, Radius = 10cm. Coefficient of friction = 0.4.

(a) 0.25 s

(b) 0.05 s

(c) 0.5 s

(d) 1 s

I got this question in an interview.

My enquiry is from Rolling Motion in portion System of Particles and Rotational Motion of Physics – Class 11

Answer 1

Right choice is (a) 0.25 s

Easy explanation: Friction force will decrease its linear velocity & increase its angular velocity.

f = Ma .                                                                                                                                                                          Friction ‘f’ = μN = 0.4*1*10 = 4N.

Thus, v = v0 – at  &  w = w0 + (a/R)t.

For pure rolling v = wR,

thus: v0 – at = R(w0 + (a/R)t).                                                                                                                                                                 a = f/M                                                                                                                                                                                         ∴ 5 – 4/1 = 0.1(0 + (4/0.1)t)

∴ 10 = 40t

OR t = 0.25 s.