List of top Physics Questions on Moment Of Inertia asked in JEE Main

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:

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:

A rod of linear mass density $ \lambda $ and length $ L $ is bent into the form of a ring of radius $ R $. The moment of inertia of the ring about any of its diameters is:

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 ____.

A block of mass 5 kg is placed on a rough inclined surface as shown in the figure.

If $\vec{F_1}$ is the force required to just move the block up the inclined plane and $\vec{F_2}$ is the force required to just prevent the block from sliding down, then the value of $|\vec{F_1}| - |\vec{F_2}|$ is: [Use $g = 10 \, \text{m/s}^2$]

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 ____ $\text{kg} \, \text{m}^2$

Consider the system shown. Find the moment of inertia about the diagonal shown.

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 ______.

$I _{ CM }$ is the moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc $I_{A B}$ is it's moment of inertia about an axis $AB$ perpendicular to plane and parallel to axis $CM$ at a distance $\frac{2}{3} R$ from center Where $R$ is the radius of the dise The ratio of $I _{ AB }$ and $I _{ CM }$ is $x: 9$ The value of $x$ is______

Two discs of same mass and different radii are made of different materials such that their thicknesses are 1 cm and 0.5 cm respectively. The densities of materials are in the ratio 3:5. The moment of inertia of these discs respectively about their diameters will be in the ratio of $\frac{x}{6}$. The value of x is ____.

If a solid sphere of mass $5 kg$ and a disc of mass $4 kg$ have the same radius Then the ratio of moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent will be $\frac{x}{7}$ The the value of $x$ is ___

Solid sphere $A$ is rotating about an axis $PQ$ If the radius of the sphere is $5 cm$ then its radius of gyration about $PQ$ will be $\sqrt{x} cm$ The value of $x$ is __

Solid sphere A is rotating about an axis PQ.If the radius of the sphere is 5cm then its radius of gyration about PQ will be √xcm.The value of x is

Moment of inertia of a disc of mass $M$ and radius $R$ about any of its diameters is $\frac{MR^2}{4}$. The moment of inertia of this disc about an axis normal to the disc and passing through a point on its edge will be, $\frac{x}{2}MR^2$. The value of $x$ is _________.

Find moment of inertia about axis shown which is equidistant from both spheres

A uniform solid cylinder with radius $R$ and length $L$ has a moment of inertia $I_1$ about the axis of the cylinder. A concentric solid cylinder of radius $R' = \frac{R}{2}$ and length $L' = \frac{L}{2}$ is carved out of the original cylinder. If $I_2$ is the moment of inertia of the carved-out portion, then $\frac{I_1}{I_2} =$
(Both $I_1$ and $I_2$ are about the axis of the cylinder.)

What is the center of gravity of a semi-circular disc of radius (R)?

Find moment of inertia about axis shown which is equidistant from both spheres

Match List-I with List-II.

	List - I		List - II
A.	Moment of inertia of solid sphere of Radius R about any tangent	i.	$\frac{5}{3}MR^2$
B.	Moment of inertia of hollow sphere of radius (R) about any tangent	ii.	$\frac{7}{5}MR^2$
C.	Moment of inertia of circular ring of radius (R) about its diameter	iii.	$\frac{1}{4}MR^2$
D.	Moment of inertia of circular disc of radius (R) about any diameter	iv.	$\frac{1}{2}MR^2$

Choose the correct answer from the options given below.

The moment of inertia of a uniform thin rod about a perpendicular axis passing through one end is I₁. The same rod is bent into a ring and its moment of inertia about a diameter is I₂. If
$\frac{I_1}{I_2}$ is $\frac{xπ²}{3}$
then the value of x will be ______.

Two small spheres each of mass 10 mg are suspended from a point by threads 0.5 m long. They are equally charged and repel each other to a distance of 0.20 m. The charge on each of the sphere is $\frac{a}{21} \times 10^{-8} C$.
The value of 'a' will be ______. [Given g = 10 ms–2]

Three solid spheres each of mass $m$ and diameter $d$ are stuck together such that the lines connecting the centres form an equilateral triangle of side of length $d$. The ratio $I_0/I_A$ of moment of inertia $I_0$ of the system about an axis passing the centroid and about center of any of the spheres $I_A$ and perpendicular to the plane of the triangle is :

Two identical spherical balls of mass $M$ and radius $R$ each are stuck on two ends of a rod of length $2R$ and mass $M$ (see figure). The moment of inertia of the system about the axis passing perpendicularly through the centre of the rod is :

Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:

Moment of inertia of an equilateral triangular lamina $ABC$, about the axis passing through its centre $O$ and perpendicular to its plane is $I_o$ as shown in the figure. A cavity $DEF$ is cut out from the lamina, where $D, E, F$ are the mid points of the sides. Moment of inertia of the remaining part of lamina about the same axis is :

A vessel contains a mixture of $1$ mole of oxygen and two moles of nitrogen at $300 \,K$. The ratio of the rotational kinetic energy per $ O_{2} $ molecule to that per $ N_{2} $ molecule is