Question

Figure (10-Q6) shows a smooth inclined plane fixed in a car accelerating on a horizontal road. The angle of incline θ is related to the acceleration a of the car as a = g tanθ. If the sphere is set in pure rolling on the incline,
(a) it will continue pure rolling
(b) it will slip down the plane
(c) its linear velocity will increase
(d) its linear velocity will slowly decrease.
Figure

Answer 1

(a) it will continue pure rolling



From the free body diagram of sphere, we have:
Net force on the sphere along the incline,
F_net = mgsinθ − macosθ ...(i)
On putting a = gtanθ in equation (i), we get:
F_net = 0
Therefore, if the sphere is set in pure rolling on the incline, it will continue pure rolling.