Q: Problem Statement

A solid cylinder of mass $ m = 2 \, \text{kg} $ and radius $ r = 0.1 \, \text{m} $ rolls down an inclined plane without slipping. Find the acceleration of the cylinder.

Q: Solution

The moment of inertia for a solid cylinder is $ I = \frac{1}{2} mr^2 $. Substitute this into the acceleration formula:

Question 1

Problem Statement

Accepted Answer

A solid cylinder of mass $ m = 2 \, \text{kg} $ and radius $ r = 0.1 \, \text{m} $ rolls down an inclined plane without slipping. Find the acceleration of the cylinder.

Question 2

Concepts Involved

Accepted Answer

For rolling motion without slipping, the acceleration is given by $ a = \frac{g \sin \theta}{1 + \frac{I}{mr^2}} $, where $ I $ is the moment of inertia of the cylinder.

Question 3

Solution

Accepted Answer

The moment of inertia for a solid cylinder is $ I = \frac{1}{2} mr^2 $. Substitute this into the acceleration formula:

Question 4

Key Takeaways

Accepted Answer

Understanding the moment of inertia and its role in rotational motion is crucial. Always consider the angle of inclination in problems involving inclined planes.

JUPITER SCIENCE

10 Physics Numerical Problems with Solutions for IIT JEE Preparation

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