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 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. Correct Answer 2/3 s

Friction force ‘f’ will cause its speed to come down & increase its angular speed till V=Rw. f = μN = 0.3*2*10 = 6N. Thus, deceleration ‘a’ = 6/2 = 3m/s2. And, angular acceleration = a/R = 3/0.05 = 60 rad/s2. 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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