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The answer key says that the correct answer is F =[mg*SQRT(2RH-H^2)]/r-h

I know that mg is gravity so the force of gravity plays a role here. I don't know the direction of friction because F is pointing right, but the object also rotates clockwise. Friction would resist the sliding but would contribute to the rotation.

I know torque is the cross product of R and F. I have no idea though why we have SQRT(2RH-H^2). I don't know what to do. Am I suppose to work with torque somehow?