Question

There is a step of height `h` on an incline plane. The step prevents a ball of radius `R` from rolling down. If the inclination `(theta)` to the incline is increased gradualluy, at some value of `theta` the ball will just manage to climb the step then value of `theta` is.

A. `costheta = (R)/(R + h)`
B. `costheta = (R - h)/(R)`
C. `costheta = (R - 2h)/(R)`
D. `sintheta = (R - h)/(R)`

Answer 1

Correct Answer - B
(a) The ball begin to climb the step if the line of action of its weight `(Mg)` passes to the left to point `A`. This will cause an unbalanced torque about `A`.
In critical case (see figure) `costheta = (R - h)/(R)`

(b) In the position shown, the `COM` of the ball is vertically above point `A` at a distance `R`. As the ball climbs, its centre of mass will lover from this position. (Otherwise why will the ball come down?) In the position shown the centre of mass is at highest position.