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
• B. AB = 2v
• C. AB = 4v
• D. If v >$\sqrt { 4 \mathrm { rg } }$, the blob of mud will land on the wheel and not on the road.

Answer 1

Answer: (C)

AB = 4v

Answer 2

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 = $\frac { 1 } { 2 }$ gt²

or t = and AB = (2v)t.