Question

A wheel of radius r rolls without slipping with a speed v on a horizontal road. When it is at a point A on the road, a small blob of mud separates from the wheel at its highest point and lands at point B on the road.

(a) AB = v√r/g

(b) AB = 2v√r/g

(c) AB = 4v√r/g

(d) If v = √4rg, the blob of mud will land on the wheel and not on the road. 

Answer 1

Correct Answer is: (c) AB = 4v√r/g

At the point of leaving the wheel, the blob of mud is at a height 2r above the road and has a horizontal velocity 2v.

Let t = time of travel from D to B. Then, 2r = 1/2 gt².

or t = 2√r/g and AB = (2v) t.