The moment of inertia of a uniform circular disc of radius R and mass M about an axis passing from the edge of the disc and normal to the disc is:
\(\frac{5}{2}MR^2\)
\(MR^2\)
\(\frac{7}{2}MR^2\)
\(\frac{3}{2}MR^2\)
The Correct Option is D
Solution and Explanation
Moment of inertia of the disc around an axis perpendicular to its plane and passing through its centre of mass ICM = \(\frac{1}{2}\) MR2
The disc's moment of inertia about an axis perpendicular to its plane and running across its diameter may be calculated using the parallel axis theorem by using the formula I = ICM + Md2.
Therefore, I = \(\frac{1}{2}\) MR2+MR2 = \(\frac{3}{2}MR^2\).
Correct option is (D): \(\frac{3}{2}MR^2\)
Top Questions on 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
- Two iron solid discs of negligible thickness have radii \( R_1 \) and \( R_2 \) and moment of inertia \( I_1 \) and \( I_2 \), respectively. For \( R_2 = 2R_1 \), the ratio of \( I_1 \) and \( I_2 \) would be \( \frac{1}{x} \), where \( x \) is:
- JEE Main - 2025
- Physics
- System of Particles & Rotational Motion
A string of length \( L \) is fixed at one end and carries a mass of \( M \) at the other end. The mass makes \( \frac{3}{\pi} \) rotations per second about the vertical axis passing through the end of the string as shown. The tension in the string is ________________ ML.
- JEE Main - 2025
- Physics
- System of Particles & Rotational Motion
- The center of mass of a thin rectangular plate (fig - x) with sides of length \( a \) and \( b \), whose mass per unit area (\( \sigma \)) varies as \( \sigma = \sigma_0 \frac{x}{ab} \) (where \( \sigma_0 \) is a constant), would be
- JEE Main - 2025
- Physics
- System of Particles & Rotational Motion
- A body of mass 10 kg is moving with a speed of 5 m/s. What is the momentum of the body?
- VITEEE - 2025
- Physics
- System of Particles & Rotational Motion
Questions Asked in NEET exam
The current passing through the battery in the given circuit, is:
- NEET (UG) - 2025
- Current electricity
A bob of heavy mass \(m\) is suspended by a light string of length \(l\). The bob is given a horizontal velocity \(v_0\) as shown in figure. If the string gets slack at some point P making an angle \( \theta \) from the horizontal, the ratio of the speed \(v\) of the bob at point P to its initial speed \(v_0\) is :
- NEET (UG) - 2025
- Pendulums
- 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
- The intensity of transmitted light when a polaroid sheet, placed between two crossed polaroids at \(22.5^\circ\) from the polarization axis of one of the polaroids (\(I_0\) is the intensity of polarised light after passing through the first polaroid):
- NEET (UG) - 2025
- Polarization
A full wave rectifier circuit with diodes (\(D_1\)) and (\(D_2\)) is shown in the figure. If input supply voltage \(V_{in} = 220 \sin(100 \pi t)\) volt, then at \(t = 15\) msec:
- NEET (UG) - 2025
- Semiconductor Diode
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