Find moment of inertia about axis shown which is equidistant from both spheres
Find moment of inertia about axis shown which is equidistant from both spheres
Solution and Explanation
88/500
Top Questions on Moment Of Inertia
- The moment of inertia of a circular ring of mass $ M $ and diameter $ r $ about a tangential axis lying in the plane of the ring is:
- JEE Main - 2025
- Physics
- Moment Of Inertia
- When a body is dropped from height H, the time taken to reach the ground is T. What is the time taken to reach height H/2 from the ground?
- KEAM - 2025
- Physics
- Moment Of Inertia
- Moment of inertia of a disc about the axis passing through the center and perpendicular to the plane is \(I_1\). What is the moment of inertia about its diameter?
- KEAM - 2025
- Physics
- Moment Of Inertia
- What is the moment of inertia of a solid sphere of mass \( M \) and radius \( R \) about its diameter?
- MHT CET - 2025
- Physics
- Moment Of Inertia
A, B and C are disc, solid sphere and spherical shell respectively with the same radii and masses. These masses are placed as shown in the figure.
The moment of inertia of the given system about PQ is $ \frac{x}{15} I $, where $ I $ is the moment of inertia of the disc about its diameter. The value of $ x $ is:- JEE Main - 2025
- Physics
- Moment Of Inertia
Questions Asked in JEE Main exam
- Identify A, B, and C in the given reaction sequence: \[ \text{A} \xrightarrow{\text{HNO}_3} \text{Pb(NO}_3)_2 \xrightarrow{\text{H}_2\text{SO}_4} \text{B} \rightarrow \text{C (Yellow ppt)}. \]
- JEE Main - 2025
- Chemical Reactions
Consider the following molecules:
The order of rate of hydrolysis is:- JEE Main - 2025
- Hydrolysis of salts
- If \( z_1, z_2, z_3 \in \mathbb{C} \) are the vertices of an equilateral triangle, whose centroid is \( z_0 \), then \( \sum_{k=1}^{3} (z_k - z_0)^2 \) is equal to
- JEE Main - 2025
- complex numbers
Two cells of emf 1V and 2V and internal resistance 2 \( \Omega \) and 1 \( \Omega \), respectively, are connected in series with an external resistance of 6 \( \Omega \). The total current in the circuit is \( I_1 \). Now the same two cells in parallel configuration are connected to the same external resistance. In this case, the total current drawn is \( I_2 \). The value of \( \left( \frac{I_1}{I_2} \right) \) is \( \frac{x}{3} \). The value of x is 1cm.
- JEE Main - 2025
- Current electricity
Let A = \(\begin{bmatrix} \log_5 128 & \log_4 5 \log_5 8 & \log_4 25 \end{bmatrix}\) \). If \(A_{ij}\) is the cofactor of \( a_{ij} \), \( C_{ij} = \sum_{k=1}^2 a_{ik} A_{jk} \), and \( C = [C_{ij}] \), then \( 8|C| \) is equal to:
- JEE Main - 2025
- Applications of Determinants and Matrices
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