Find moment of inertia about axis shown which is equidistant from both spheres
Correct Answer: 88500
Solution and Explanation
\(I=[\frac{2}{5}Mr^{2}+M(0.2)^{2}]\times 2\)
\(=[\frac{2}{5}\times 2\times (0.1)^{2}+2\times (0.2)^{2}]\times 2\)
\(=[\frac{4}{500}+\frac{8}{100}]\times 2\)
\(=\frac{44\times 2}{500}=\frac{88}{500}(kg-m^{2})\)
So, the correct answer is \(\frac{88}{500} (kg-m^{2})\)
Top Questions on 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
- A solid cylinder and a hollow cylinder, each of mass \( M \) and radius \( R \), are rotating with the same angular velocity \( \omega \). What is the ratio of their rotational kinetic energies \( \left( \frac{K_{\text{hollow}}}{K_{\text{solid}}} \right) \)?
- MHT CET - 2025
- Physics
- Moment Of Inertia
Questions Asked in JEE Main exam
The total number of structural isomers possible for the substituted benzene derivatives with the molecular formula $C_7H_{12}$ is __
- JEE Main - 2025
- Organic Chemistry
Four capacitors each of capacitance $16\,\mu F$ are connected as shown in the figure. The capacitance between points A and B is __ (in $\mu F$)
- JEE Main - 2025
- Electrostatics
Among, Sc, Mn, Co and Cu, identify the element with highest enthalpy of atomisation. The spin only magnetic moment value of that element in its +2 oxidation state is _______BM (in nearest integer).
- JEE Main - 2025
- d block elements
X g of nitrobenzene on nitration gave 4.2 g of m-dinitrobenzene. X =_____ g. (nearest integer) [Given : molar mass (in g mol\(^{-1}\)) C : 12, H : 1, O : 16, N : 14]
- JEE Main - 2025
- Stoichiometry and Stoichiometric Calculations
A perfect gas (0.1 mol) having \( \bar{C}_V = 1.50 \) R (independent of temperature) undergoes the above transformation from point 1 to point 4. If each step is reversible, the total work done (w) while going from point 1 to point 4 is ____ J (nearest integer) [Given : R = 0.082 L atm K\(^{-1}\)]
- JEE Main - 2025
- Thermodynamics
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