Question:
Four identical discs each of mass ‘M’ and diameter ‘a’ are arranged in a small plane as shown in the figure. If the moment of inertia of the system about OO’ is (\(\frac{x}{4}\)) Ma2. Then, the value of x will be _______.
Four identical discs each of mass ‘M’ and diameter ‘a’ are arranged in a small plane as shown in the figure. If the moment of inertia of the system about OO’ is (\(\frac{x}{4}\)) Ma2. Then, the value of x will be _______.
Updated On: Mar 19, 2025
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Correct Answer: 3
Solution and Explanation
I=\(2\times\frac{Ma^2}{\frac{2}{4}}\)+\(2\times\frac{Ma^2}{\frac{2}{4}}\)+\(\frac{Ma^2}{2}\)
=\(\frac{Ma^2}{8}\)+5\(\frac{Ma^2}{8}\)
=6\(\frac{Ma^2}{8}\)
=\(\frac{3}{4}\) Ma2
=\(\frac{Ma^2}{8}\)+5\(\frac{Ma^2}{8}\)
=6\(\frac{Ma^2}{8}\)
=\(\frac{3}{4}\) Ma2
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Concepts Used:
Rotational Motion
Rotational motion can be defined as the motion of an object around a circular path, in a fixed orbit.
Rotational Motion Examples:
The wheel or rotor of a motor, which appears in rotation motion problems, is a common example of the rotational motion of a rigid body.
Other examples:
- Moving by Bus
- Sailing of Boat
- Dog walking
- A person shaking the plant.
- A stone falls straight at the surface of the earth.
- Movement of a coin over a carrom board
Types of Motion involving Rotation:
- Rotation about a fixed axis (Pure rotation)
- Rotation about an axis of rotation (Combined translational and rotational motion)
- Rotation about an axis in the rotation (rotating axis)