What is the torque from the weight of the sphere about the center of the sphere?What is the torque from the frictional force about the center of the sphere? **Problem 75: Static Equilibrium of a Sphere**A horizontal force \( \vec{F} \) is applied to a uniform sphere in a direction exactly toward the center of the sphere, as shown in the diagram. Find the magnitude of this force so that the sphere remains in static equilibrium. What is the frictional force of the incline on the sphere?**Diagram Description:**- **Sphere:** The diagram features a sphere of mass \( M \) and radius \( R \) placed on an inclined plane.- **Incline:** The incline is at an angle \( \theta \) with the horizontal.- **Force \( \vec{F} \):** A horizontal force is applied from the left side toward the center of the sphere.- **Incline and Sphere Interaction:** The contact point between the sphere and the incline indicates where friction acts upward against the sphere, opposing any potential sliding due to applied forces.**Objective:**To find the magnitude of the horizontal force \( \vec{F} \) such that the sphere remains in static equilibrium, and to calculate the frictional force exerted by the incline on the sphere.

Answered: Image /qna-images/answer/9e912243-2feb-40c3-b53a-36f9fa8680dd.jpgApplying Newton’s second law along inclined plane: Fcosθ-Mgsinθ=0 F=Mgsinθcosθ F=Mgtanθ All the forces acting along the center of the sphere except friction force which is acting along the inclined plane. Therefore, net torque on the sphere would zero which leads friction to zero. Since, net torque on the sphere would zero, therefore friction force of inclined plane would be zero.Answer: F=Mgtanθ Friction force of inclined plane = 0