Question:
One quarter section is cut from a uniform circular disc of radius R. This section has a mass M. It is made to rotate about a line perpendicular to its plane and passing through the centre of the original disc. Its moment of inertia about the axis of rotation is
One quarter section is cut from a uniform circular disc of radius R. This section has a mass M. It is made to rotate about a line perpendicular to its plane and passing through the centre of the original disc. Its moment of inertia about the axis of rotation is
Updated On: Jun 14, 2022
- $\frac{1}{2}MR^2$
- $\frac{1}{4}MR^2$
- $\frac{1}{8}MR^2$
- $\sqrt 2 MR^2 $
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The Correct Option is A
Solution and Explanation
Mass of the whole disc = 4M
Moment of inertia of the disc about the given axis
$ \, \, \, \, \, \, \, \, \, = \frac{1}{2} (4M) R^2 = 2MR^2$
$ \therefore $ Moment of inertia of quarter section of the disc
$ \, \, \, \, \, \, \, \, \, = \frac{1}{4} (2M R^2 )= \frac{1}{2}MR^2$
Moment of inertia of the disc about the given axis
$ \, \, \, \, \, \, \, \, \, = \frac{1}{2} (4M) R^2 = 2MR^2$
$ \therefore $ Moment of inertia of quarter section of the disc
$ \, \, \, \, \, \, \, \, \, = \frac{1}{4} (2M R^2 )= \frac{1}{2}MR^2$
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Concepts Used:
System of Particles and Rotational Motion
- The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
- The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
- The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.