Question

A solid sphere, hollow sphere, and solid cylinder start sliding from an inclined plane without rolling. Then the ratio of time taken by them to reach the ground is?

• A. 1:2:3
• B. 1:1:1
• C. 1:3:2
• D. 3:2:1

Hint:

Objects with lower moments of inertia reach the ground faster when sliding down an inclined plane.

Answer 1

The Correct Option is C

The time taken for a rolling object to reach the ground depends on its moment of inertia. The body with the smallest moment of inertia will reach the ground first.

1. Step 1: Understand the concept. - The time taken for an object to roll down an inclined plane depends on its moment of inertia. The greater the moment of inertia, the slower it will reach the ground.

2. Step 2: Compare the moments of inertia. - For a solid sphere, the moment of inertia is \( \frac{2}{5}mr^2 \). - For a hollow sphere, the moment of inertia is \( \frac{2}{3}mr^2 \). - For a solid cylinder, the moment of inertia is \( \frac{1}{2}mr^2 \).

3. Step 3: Calculate the ratio of times. The ratio of times taken by the objects to reach the ground is inversely proportional to their moments of inertia. Thus, the object with the smallest moment of inertia will reach the ground first. Therefore, the ratio of times taken by the solid sphere, solid cylinder, and hollow sphere to reach the ground is 1:3:
2.