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.

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 = 3 m/s².

And, angular acceleration = a/R = 3/0.05 = 60 rad/s².

v = v_o – at = 4 – 3t.

w = w_o + (a/R)t = 0 + 60t = 60t.

At pure rolling, v = Rw

⇒ 4 – 3t = 0.05(60t)

∴ 4 = 3t + 3t = 6t.

∴ t = 2/3 s.