Question

A light cart can roll without friction on an inclined plane, A plumb-line (a sphere of mass m on a string) is mounted on the cart (Fig.). What will be the direction of the plumb-line as the car rolls freely? The string was held in a position perpendicular to the inclined plane until the cart began rolling.

Answer 1

Answer: The string will be perpendicular to the inclined plane during the rolling. 

Explanation:

The cart will roll with an acceleration a = gsina. For the sphere to have such an acceleration, it is necessary that the resultant of the force of gravity and the force due to the tension in the string, both of which are applied to the sphere (Fig. 208),

should have a direction parallel to the inclined plane and a magnitude F = ma = mgsinα. This is possible only if the string is perpendicular to the inclined plane.