A composite disc is made out of two concentric cylinders, as shown. The inner cylinder has radius 30 cm. The outer cylinder has radius 50 cm. If you pull on a light rope attached to the edge of the outer cylinder (shown left) with 100 N, how hard must you pull on a light rope attached to the edge of the inner cylinder (shown right) so the disc does not spin?

• A. 300 N
• B. 667 N
• C. 60 N
• D. 167 N

Answer: (D)

Verified step by step guidance

1. Understand that the problem involves balancing torques to prevent the disc from spinning. Torque is the rotational equivalent of force and is calculated as the product of force and the radius at which the force is applied.
2. Identify the forces and radii involved: The force applied to the outer cylinder is 100 N at a radius of 50 cm, and the force applied to the inner cylinder is unknown at a radius of 30 cm.
3. Set up the equation for torque balance: The torque from the outer cylinder must equal the torque from the inner cylinder to prevent spinning. This can be expressed as: \( F_{outer} \times r_{outer} = F_{inner} \times r_{inner} \).
4. Substitute the known values into the equation: \( 100 \text{ N} \times 50 \text{ cm} = F_{inner} \times 30 \text{ cm} \).
5. Solve for \( F_{inner} \) by rearranging the equation: \( F_{inner} = \frac{100 \times 50}{30} \). This will give you the force needed on the inner cylinder to balance the torques.