A solid sphere is given a horizontal velocity of 4m/s on a flat surface. What will be its velocity when it starts pure rolling? Mass = 2kg, Radius = 5cm. Coefficient of friction = 0.3.(a) It cannot roll purely(b) 2/3 s(c) 2s(d) 3sI have been asked this question at a job interview.Query is from Rolling Motion in section System of Particles and Rotational Motion of Physics – Class 11

A solid sphere is given a horizontal velocity of 4m/s on a flat surfac

1.	A solid sphere is given a horizontal velocity of 4m/s on a flat surface. What will be its velocity when it starts pure rolling? Mass = 2kg, Radius = 5cm. Coefficient of friction = 0.3.(a) It cannot roll purely(b) 2/3 s(c) 2s(d) 3sI have been asked this question at a job interview.Query is from Rolling Motion in section System of Particles and Rotational Motion of Physics – Class 11
Answer» Correct option is (b) 2/3 s Easy explanation: Friction force ‘f’ will cause its speed to come down & increase its angular speed till V=Rw. f = μN = 0.3210 = 6N. Thus, deceleration ‘a’ = 6/2 = 3m/s^2. And, angular ACCELERATION = a/R = 3/0.05 = 60 rad/s^2. v = V0 – at = 4 – 3T. w = w0 + (a/R)t = 0 + 60t = 60t. At PURE rolling, v=Rw ⇒ 4 – 3t = 0.05(60t) ∴ 4 = 3t + 3t = 6t. ∴ t = 2/3 s.

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