Question:
Two identical concentric rings each of mass $m$ and radius $R$ are placed perpendicularly. What is the moment of inertia about axis of one of the rings
Two identical concentric rings each of mass $m$ and radius $R$ are placed perpendicularly. What is the moment of inertia about axis of one of the rings
Updated On: Jun 18, 2022
- $\frac{3}{2}MR^2$
- $2MR^2$
- $3MR^2$
- $\frac{1}{4}MR^2$
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Since the axis of two rings are also perpendicular to each other, therefore applying the theorem of perpendicular axes
$I=M R^{2}+\frac{1}{2} M R^{2}$
$\frac{3}{2} M R^{2}$
$I=M R^{2}+\frac{1}{2} M R^{2}$
$\frac{3}{2} M R^{2}$
Was this answer helpful?
0
0
Top Questions on Moment Of Inertia
- The moment of inertia of a thin rod about an axis passing through its mid point and perpendicular to the rod is 2400 g cm2. The length of the 400 g rod is nearly :
- NEET (UG) - 2024
- Physics
- Moment Of Inertia
- The radius of gyration of a solid sphere of mass \(5 \, \text{kg}\) about \(XY\) is \(5 \, \text{m}\) as shown in figure.
The radius of the sphere is \(\frac{5x}{\sqrt{7}} \, \text{m}\), then the value of \(x\) is:
- NEET (UG) - 2024
- Physics
- Moment Of Inertia
- Three balls of masses $2 \, \text{kg}$, $4 \, \text{kg}$, and $6 \, \text{kg}$ respectively are arranged at the centre of the edges of an equilateral triangle of side $2 \, \text{m}$.The moment of inertia of the system about an axis through the centroid and perpendicular to the plane of the triangle, will be ____ $\text{kg} \, \text{m}^2$
- JEE Main - 2024
- Physics
- Moment Of Inertia
- A string is wrapped around the rim of a wheel of moment of inertia $0.40 \, \text{kgm}^2$ and radius $10 \, \text{cm}$. The wheel is free to rotate about its axis. Initially, the wheel is at rest. The string is now pulled by a force of $40 \, \text{N}$. The angular velocity of the wheel after $10 \, \text{s}$ is $x \, \text{rad/s}$, where $x$ is ______.
- JEE Main - 2024
- Physics
- Moment Of Inertia
- Two identical spheres each of mass 2 kg and radius 50 cm are fixed at the ends of a light rod so that the separation between the centers is 150 cm. Then, moment of inertia of the system about an axis perpendicular to the rod and passing through its middle point is \(\frac{x}{20}\) kg m3 , where the value of x is ____.
- JEE Main - 2024
- Physics
- Moment Of Inertia
View More Questions
Questions Asked in DUET exam
- A hammer of mass $200\, kg$ strikes a steel block of mass $200\, g$ with a velocity $8\, ms^{-1}$. If $23\%$ of the energy is utilized to heat the steel block, the rise in temperature of the block is (specific heat capacity of steel = $460 \; J \; kg^{-1} \; K^{-1}$)
- DUET - 2019
- specific heat capacity
- What is the shape and magnetic nature of permanganate ion ?
- DUET - 2019
- d -and f -Block Elements
- The mobility of charge carriers increases with
- DUET - 2011
- Electric Current
- Phagocytosis and pinocytosis are collectively termed as
- DUET - 2011
- Cell: the unit of life
- How many $ 1\,\mu F $ capacitors must be connected in parallel to store a charge of $1\, C$ with a potential of $110\, V$ across the capacitors?
- DUET - 2011
- electrostatic potential and capacitance
View More Questions
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