Question

26. A small block of mass m is placed inside a
smooth hollow sphere of radius R at lowest
position. Initially system was at rest as shown in
the figure. Now the sphere is given a constant
horizontal acceleration g by an external agent.
The maximum angular displacement of block with
vertical, w.r.t. sphere is
(1) 60°
(3) 45°
(2) 30°
(4) 90°

Answer 1

Thus the value of θ = tan^-1 (2)

Explanation:

The rotational motion of the hollow cylinder will have radius r and the angle for motion be alpha. then the maximum angular displacement be given by the equation of rotational motion which will be

μ^2 sin^2 θ / g = μ^2 sin^2 θ / 2g

2 sin θ . cos θ = sin^2 θ / cos θ = 2"

tan θ = 2

θ = tan^-1 (2)