Question

A sphere cannot roll on
(1) A smooth horizontal plane
(2) A rough horizontal plane
(3) A smooth inclined plane
(4). All of these

Answer 1

When a body continues to roll on a surface with acceleration a, it must have an angular acceleration $\alpha$ and if it has an angular acceleration $\alpha$ it must have an acceleration a, with the relation $a=\alpha R$ where the radius of the body. We should look for such a relationship in all of the above cases listed in the options, and if one cannot be found, the body cannot roll.

Complete answer:
1.Consider a smooth inclined surface with a ball with a radius of.
2.The ball will be subjected to the following forces: The component of weight along the plane will be a force on the sphere that can accelerate the sphere, and the component of weight along the plane will be a force on the sphere that will be perpendicular to the surface, and the normal reaction force will be perpendicular to the surface.
3.As a result, $a \neq 0$ . Because both of these forces (normal reaction and weight) pass through the center of the ball, the torque on the ball around the center will be zero as well, implying that $\alpha=0$.
4.As a result of the values being such that $a \neq \alpha R$, rolling motion.

So the correct option is (3) .

Note:
Students frequently make the mistake of not connecting physics to everyday phenomena while solving such questions, but mathematical equations are required to judge events that are not possible in everyday life, such as a horizontal smooth surface. Second, the condition $a=\alpha R$ gives us the equation for rolling motion to continue; however, if there is slipping at the outset and we want rolling motion to begin, rolling motion always begins when the condition is met, where $v$ denotes the object's speed and omega denotes the angular speed. Once rolling motion starts the condition $a=\alpha R$ is used to decide whether the ball will continue to roll.