Rotational Motion
Moment of inertia of a circular disc around its diameter having mass M and radius R is:
2MR2
MR2 / 2
Option 4 : MR2 / 4
CT 1: हिन्दी (आदिकाल)
Moment of inertia:
​Moment of inertia is defined as the quantity of the body resisting angular acceleration and it is given by the product of the mass of every particle with its square of a distance from the axis of rotation.
Perpendicular axis theorem:
The perpendicular axis theorem states that the moment of inertia of a planar lamina about an axis perpendicular to the plane of the lamina is equal to the sum of the moments of inertia of the lamina about the two axes at right angles to each other, in its own plane intersecting each other at the point where the perpendicular axis passes through it.
​⇒ IZ = IX + IY
CALCULATION:
We know that the moment of inertia of a circular disc about its axis is given as,
\(⇒ I_{Z}=\frac{MR^{2}}{2}\) -----(1)
Where M = mass of the disc, and R = radius of the disc
By perpendicular axis theorem for a circular disc,
⇒ IZ = IX + IY -----(2)
Where IX and IY is the moment of inertia of the circular disc about its diameter
Since the circular disc is symmetrical about its diameter so,
⇒ IX = IY = I -----(3)
By equation 1, equation 2, and equation 3,
\(\Rightarrow I + I=\frac{MR^{2}}{2}\)
\(\Rightarrow 2I=\frac{MR^{2}}{2}\)
\(\Rightarrow I=\frac{MR^{2}}{4}\)
Hence, option 4 is correct.
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