Solution: A uniform rod of mass m and length l is pivoted about a horizontal, frictionless pin at the end of a thin extension (of negligible mass) a distance l from the center of mass of the rod. The rod is rel

A uniform rod of mass m and length l is pivoted about a horizontal, frictionless pin at the end of a thin extension (of negligible mass) a distance l from the center of mass of the rod. The rod is released from rest at an angle of θ with the horizontal, as shown in the figure.

What is the magnitude of the Horizontal force F_{x} exerted on the pivot end of the rod extension at the instant the rod is in a horizontal position? The acceleration due to gravity is g and the moment of inertia of the rod about its center of mass is 1/12 mℓ^{2}.

1. F_{x} = 1/13 mg sin(θ)

2. F_{x} = 24/13 mg cos(θ)

3. F_{x} = 24/13 mg sin(θ)

4. F_{x} = 13/12 mg cos(θ)

5. F_{x} = 12/13 mg cos(θ)

6. F_{x} = 12/13 mg sin(θ)

7. F_{x} = 13/12 mg sin(θ)

8. F_{x} = mg cos(θ)

9. F_{x} = 1/13 mg cos(θ)

10. F_{x} = mg sin(θ)