Question:
The moment of inertia of a thin uniform circular disc about one of the diameters is $l$. Its moment of inertia about an axis perpendicular to the plane of the disc and passing through its centre is
The moment of inertia of a thin uniform circular disc about one of the diameters is $l$. Its moment of inertia about an axis perpendicular to the plane of the disc and passing through its centre is
Updated On: Aug 1, 2022
- $\left(\sqrt{2}\right)I$
- $2I$
- $I/2$
- $I/\sqrt{2}$
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The Correct Option is B
Solution and Explanation
Moment of inertia of thin uniform circular disc about one of its diameter is $I$
$\therefore I=\frac{MR^{2}}{4} \dots(i)$
where M is the mass and R is the radius of the disc. Moment of inertia of disc about an axis passing through the centre and perpendicular to the plane of the disc is $I$'
$I' =\frac{MR^{2}}{2}=2 \left(\frac{MR^{2}}{4}\right)=2I$
[Using $(i)]$
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Concepts Used:
Moment of Inertia
Moment of inertia is defined as the quantity expressed by the body resisting angular acceleration which is the sum of the product of the mass of every particle with its square of a distance from the axis of rotation.
Moment of inertia mainly depends on the following three factors:
- The density of the material
- Shape and size of the body
- Axis of rotation
Formula:
In general form, the moment of inertia can be expressed as,
I = m × r²
Where,
I = Moment of inertia.
m = sum of the product of the mass.
r = distance from the axis of the rotation.
M¹ L² T° is the dimensional formula of the moment of inertia.
The equation for moment of inertia is given by,
I = I = ∑mi ri²
Methods to calculate Moment of Inertia:
To calculate the moment of inertia, we use two important theorems-
- Perpendicular axis theorem
- Parallel axis theorem