List of top Physics Questions on 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:

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 sphere of radius R is cut from a larger solid sphere of radius 2R as shown in the figure. The ratio of the moment of inertia of the smaller sphere to that of the rest part of the sphere about the Y-axis is :

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) $?

As shown in the figure, two thin coplanar circular discs A and B each of mass 'M' and radius 'r' are attached to form a rigid body. The moment of inertia of this system about an axis perpendicular to the plane of disc B and passing through its centre is

A solid sphere of mass $M$ and radius $R$ is rotating about its diameter. What is its moment of inertia about the same axis?

A person sitting inside an elevator performs a weighing experiment with an object of mass $ 50 \, \text{kg} $. Suppose that the variation of the height $ y $ (in m) of the elevator, from the ground, with time $ t $ (in s) is given by $$ y = 8\left[1 + \sin\left(\frac{2\pi t}{T}\right)\right], $$ where $ T = 40\pi \, \text{s} $. Taking acceleration due to gravity, $ g = 10 \, \text{m/s}^2 $, the maximum variation of the object's weight (in N) as observed in the experiment is ____.

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?

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?

What is the moment of inertia of a solid sphere of mass $ M $ and radius $ R $ about its diameter?

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 ______.

The radius of gyration of a solid sphere of mass $5 \, \text{kg}$ about $XY$ is $5 \, \text{m}$ as shown in figure.
The radius of the sphere is $\frac{5x}{\sqrt{7}} \, \text{m}$, then the value of $x$ is:

The moment of inertia of a cube of mass $ m $ and side $ a $ about one of its edges is equal to:

Three particles of each mass $ m $ are kept at the three vertices of an equilateral triangle of side $ 1 $. The moment of inertia of the system of the particles about any side of the triangle is:

Four identical thin, square metal sheets, S1, S2, S3 and S4, each of side a are kept parallel to each other with equal distance $d (≪ a)$ between them, as shown in the figure. Let $C_0 = \epsilon_0\frac{a^2}{d}, $where $\epsilon_0$ is the permittivity of free space.

Match the quantities mentioned in List-I with their values in List-II and choose the correct option.

List-I		List-II
P	The capacitance between S1 and S4, with S2 and S3 not connected, is	I	$3C_0$
Q	The capacitance between S1 and S4, with S2 shorted to S3, is	II	$\frac{C_0}{2}$
R	The capacitance between S1 and S3, with S2 shorted to S4, is	III	$\frac{C_0}{3}$
S	The capacitance between S1 and S2, with S3 shorted to S1, and S2 shorted to S4, is	IV	$2\frac{C_0}{3}$
			\[2C_0\]

The moment of inertia of a thin rod about an axis passing through its mid point and perpendicular to the rod is 2400 g cm². The length of the 400 g rod is nearly :

Radius of gyration $ K $ of a hollow cylinder of mass $ M $ and radius $ R $ about its long axis of symmetry is:

A thin circular disc of mass $ M $ and radius $ R $ is rotating in a horizontal plane about an axis passing through its center and perpendicular to its plane with angular velocity $ \omega $. If another disc of the same dimensions but of mass $ M/2 $ is placed gently on the first disc co-axially, then the new angular velocity of the system is:

For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to the sheet and passing through $ O $ (the center of mass) and $ O' $ (corner point) is:

Consider a uniformly dense spherical shell of inner radius $ a $ and outer radius $ b $. If $ M $ is the mass of the shell, the moment of inertia of the spherical shell about an axis passing through its center is: