A solid sphere is rolling without slipping on | vedclass

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(D) $1$. On a horizontal surface, for pure rolling without any external force, the acceleration of the center of mass is zero, and the angular acceler

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Friction force is always opposite to the motion of the sphere.

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(D) $1$. On a horizontal surface, for pure rolling without any external force, the acceleration of the center of mass is zero, and the angular acceleration is zero. Thus, the friction force is zero.$2$. When moving upward on an inclined plane, the sphere experiences a torque due to gravity that tends to decrease its angular velocity. Friction acts in the upward direction along the incline to provide the necessary torque to maintain pure rolling.$3$. When moving downward on an inclined plane, the sphere experiences a torque due to gravity that tends to increase its angular velocity. Friction acts in the upward direction along the incline to oppose this increase and maintain pure rolling.$4$. Friction does not always oppose the motion of the center of mass; it acts to maintain the condition of pure rolling $(v = r\omega)$. Therefore, the statement that friction force is always opposite to the motion of the sphere is incorrect.

$A$ solid sphere is rolling without slipping on a horizontal rough surface and starts rising on an inclined rough surface as shown in the figure. Assume pure rolling throughout the motion. Choose the $INCORRECT$ statement.

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