The moment of inertia of a uniform circular disc of radius R and mass M about an axis touching the disc at its diameter and normal to the disc is :
- MR2
- \(\bigg(\frac{2}{5}\bigg)\)MR2
- \(\bigg(\frac{3}{2}\bigg)\)MR2
- \(\bigg(\frac{5}{6}\bigg)\)MR2
The Correct Option is C
Solution and Explanation
The moment of inertia about an axis passing through centre of mass of disc and perpendicular to its plane is \(\text{I}_{CM}\) = \(\frac{1}{2}\)\(\text{MR}^2\)
where M is the mass of disc and R its radius. According to theorem of parallel axis, moment of inertia of circular disc about an axis touching the disc at its diameter and normal to the disc is
\(\text {I}\) = \(\text{I}_{CM}\) + \(\text{MR}^2\)
= \(\frac{1}{2}\) \(\text{MR}^2\) + \(\text{MR}^2\)
= \(\frac{3}{2}\) \(\text{MR}^2\)
Therefore, the correct option is (C): \((\frac{3}{2})\text{MR}^2\)
Top Questions on System of Particles & Rotational Motion
A cylindrical tube \(AB\) of length \(l\), closed at both ends, contains an ideal gas of \(1\) mol having molecular weight \(M\). The tube is rotated in a horizontal plane with constant angular velocity \(\omega\) about an axis perpendicular to \(AB\) and passing through the edge at end \(A\), as shown in the figure. If \(P_A\) and \(P_B\) are the pressures at \(A\) and \(B\) respectively, then (consider the temperature to be same at all points in the tube)
- JEE Main - 2026
- Physics
- System of Particles & Rotational Motion
As shown in the figure, radius of gyration about the axis shown in \(\sqrt{n}\) cm for a solid sphere. Find 'n'.
- JEE Main - 2026
- Physics
- System of Particles & Rotational Motion
When rod becomes horizontal find its angular velocity. It is pivoted at point A as shown.
- JEE Main - 2026
- Physics
- System of Particles & Rotational Motion
- The moment of inertia of a solid disc rotating along its diameter is 2.5 times higher than the moment of inertia of a ring rotating in a similar way. The moment of inertia of a solid sphere which has the same radius as the disc and rotating in similar way, is \( n \) times higher than the moment of inertia of the given ring. Here, \( n = \):
- JEE Main - 2025
- Physics
- System of Particles & Rotational Motion
- The increase in pressure required to decrease the volume of a water sample by 0.2percentage is \( P \times 10^5 \, \text{Nm}^{-2} \). Bulk modulus of water is \( 2.15 \times 10^9 \, \text{Nm}^{-2} \). The value of \( P \) is ________________.
- JEE Main - 2025
- Physics
- System of Particles & Rotational Motion
Questions Asked in NEET exam
- Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every T min. A girl is driving scooty with a speed of 60 km/h in the direction X to Y. She notices that a bus goes past her every 30 minutes in the direction of her motion, and every 10 minutes in the opposite direction. Choose the correct option for the period T of the bus service and the speed (assumed constant) of the buses.
- NEET (UG) - 2025
- Relative Velocity
- A physical quantity P is related to four observations a, b, c, and d as follows: P = a3 b2 (c / √d) The percentage errors of measurement in a, b, c, and d are 1%, 3%, 2%, and 4% respectively. The percentage error in the quantity P is:
- NEET (UG) - 2025
- Dimensional analysis and its applications
What is Microalbuminuria ?
- NEET (UG) - 2025
- Human physiology
The output (Y) of the given logic implementation is similar to the output of an/a …………. gate.
- NEET (UG) - 2025
- Logic gates
- An oxygen cylinder of volume 30 litre has 18.20 moles of oxygen. After some oxygen is withdrawn from the cylinder, its gauge pressure drops to 11 atmospheric pressure at temperature \(27^\circ\)C. The mass of the oxygen withdrawn from the cylinder is nearly equal to: [Given, \(R = \frac{100}{12} \text{ J mol}^{-1} \text{K}^{-1}\), and molecular mass of \(O_2 = 32 \text{ g/mol}\), 1 atm pressure = \(1.01 \times 10^5 \text{ N/m}^2\)]
- NEET (UG) - 2025
- Ideal-gas equation and absolute temperature
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