Question

A solid cylinder and a hollow cylinder of the equal radius and mass start rolling down (without slipping) on a fixed inclined plane from rest at the same time at the same height from the ground. Which of the following statements is correct?

• A. Solid cylinder reaches the ground earlier and with higher velocity than hollow cylinder
• B. Both solid and hollow cylinders reach at the same time with same velocity
• C. Solid cylinder reaches ground earlier (higher velocity) than hollow cylinder
• D. Hollow cylinder reaches ground earlier with higher velocity than solid cylinder

Hint:

Lower Moment of Inertia ($I$) = Faster rolling. Solid objects always beat hollow ones of the same shape.

Answer 1

The Correct Option is A

Step 1: Concept
The acceleration of a rolling object is $a = \frac{g \sin \theta}{1 + I/mR^2}$, where $I$ is the moment of inertia.

Step 2: Moment of Inertia Analysis
For a solid cylinder, $I = \frac{1}{2}mR^2$. For a hollow cylinder, $I = mR^2$.

Step 3: Reasoning
The solid cylinder has a smaller moment of inertia, meaning it resists rotational motion less. Therefore, it has a higher linear acceleration and reaches the bottom faster with higher velocity.

Step 4: Conclusion
The solid cylinder wins the race. Final Answer: (A)