Physics

Moment of Inertia

39 Questions

The moment of inertia measures the resistance of a rigid body to changes in its rotational motion. Questions cover calculating inertia for uniform cylinders, solid spheres, and thin spherical shells. This core physics topic is vital for engineering aspirants and civil services preliminary tests.

Uniform cylinder inertiaSolid sphere inertiaAngular momentum equationRigid body rotationPoint mass inertia

Moment of Inertia Questions

Multiple choice

What is the moment of inertia of a point mass?

  1. mr^2

  2. m/r^2

  3. mr

  4. m/r
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The moment of inertia of a point mass is defined as the product of the mass of the point mass and the square of the distance from the point mass to the axis of rotation.

Multiple choice

What is the moment of inertia of a rigid body?

  1. The sum of the moments of inertia of all the point masses that make up the body

  2. The product of the mass of the body and the square of the distance from the center of mass of the body to the axis of rotation

  3. The sum of the products of the masses of all the point masses that make up the body and the squares of their distances from the axis of rotation

  4. The product of the mass of the body and the square of the radius of gyration of the body
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The moment of inertia of a rigid body is defined as the sum of the products of the masses of all the point masses that make up the body and the squares of their distances from the axis of rotation.

Multiple choice

What is the moment of inertia of a point mass m at a distance r from the axis of rotation?

  1. mr

  2. mr^2

  3. m/r

  4. m/r^2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The moment of inertia of a point mass is given by I = mr^2.

Multiple choice

What is the moment of inertia of a thin rod of mass M and length L about an axis perpendicular to the rod and passing through its center?

  1. (1/12)ML^2

  2. (1/3)ML^2

  3. (1/2)ML^2

  4. ML^2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The moment of inertia of a thin rod about an axis perpendicular to the rod and passing through its center is given by I = (1/12)ML^2.

Multiple choice

What is the moment of inertia of a thin hoop of mass M and radius R about an axis perpendicular to the hoop and passing through its center?

  1. MR^2

  2. (1/2)MR^2

  3. (1/3)MR^2

  4. (1/4)MR^2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The moment of inertia of a thin hoop about an axis perpendicular to the hoop and passing through its center is given by I = MR^2.

Multiple choice

What is the moment of inertia of a solid cylinder of mass M and radius R about an axis perpendicular to the cylinder and passing through its center?

  1. (1/2)MR^2

  2. (1/3)MR^2

  3. (1/4)MR^2

  4. (1/6)MR^2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The moment of inertia of a solid cylinder about an axis perpendicular to the cylinder and passing through its center is given by I = (1/2)MR^2.

Multiple choice

What is the moment of inertia of a solid sphere of mass M and radius R about an axis passing through its center?

  1. (2/3)MR^2

  2. (2/5)MR^2

  3. (3/5)MR^2

  4. (3/4)MR^2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The moment of inertia of a solid sphere about an axis passing through its center is given by I = (2/5)MR^2.

Multiple choice

What is the moment of inertia of a hollow sphere of mass M and radius R about an axis passing through its center?

  1. (2/3)MR^2

  2. (2/5)MR^2

  3. (3/5)MR^2

  4. (3/4)MR^2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The moment of inertia of a hollow sphere about an axis passing through its center is given by I = (2/3)MR^2.

Multiple choice

What is the moment of inertia of a rectangular plate of mass M, length L, and width W about an axis perpendicular to the plate and passing through its center?

  1. (1/12)ML(L^2 + W^2)

  2. (1/3)ML(L^2 + W^2)

  3. (1/2)ML(L^2 + W^2)

  4. ML(L^2 + W^2)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The moment of inertia of a rectangular plate about an axis perpendicular to the plate and passing through its center is given by I = (1/12)ML(L^2 + W^2).

Multiple choice

What is the moment of inertia of a triangular plate of mass M, base B, and height H about an axis perpendicular to the plate and passing through its center?

  1. (1/12)MBH

  2. (1/3)MBH

  3. (1/2)MBH

  4. MBH
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The moment of inertia of a triangular plate about an axis perpendicular to the plate and passing through its center is given by I = (1/12)MBH.

Multiple choice

What is the moment of inertia of a solid cone of mass M, base radius R, and height H about an axis of symmetry?

  1. (3/10)MR^2

  2. (3/5)MR^2

  3. (1/2)MR^2

  4. (2/5)MR^2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The moment of inertia of a solid cone about an axis of symmetry is given by I = (3/10)MR^2.

Multiple choice

What is the moment of inertia of a solid hemisphere of mass M and radius R about an axis of symmetry?

  1. (2/5)MR^2

  2. (3/5)MR^2

  3. (1/2)MR^2

  4. (2/3)MR^2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The moment of inertia of a solid hemisphere about an axis of symmetry is given by I = (2/5)MR^2.

Multiple choice

What is the moment of inertia of a hollow cylinder of mass M, outer radius R1, and inner radius R2 about an axis perpendicular to the cylinder and passing through its center?

  1. (1/2)M(R1^2 + R2^2)

  2. (1/3)M(R1^2 + R2^2)

  3. (1/4)M(R1^2 + R2^2)

  4. (1/6)M(R1^2 + R2^2)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The moment of inertia of a hollow cylinder about an axis perpendicular to the cylinder and passing through its center is given by I = (1/2)M(R1^2 + R2^2).

Multiple choice

What is the moment of inertia of a thin spherical shell of mass M and radius R about an axis passing through its center?

  1. (2/3)MR^2

  2. (2/5)MR^2

  3. (3/5)MR^2

  4. (3/4)MR^2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The moment of inertia of a thin spherical shell about an axis passing through its center is given by I = (2/3)MR^2.

Multiple choice

What is the moment of inertia of a solid disk of mass M, radius R, and thickness t about an axis perpendicular to the disk and passing through its center?

  1. (1/2)MR^2 + (1/12)Mt^2

  2. (1/3)MR^2 + (1/12)Mt^2

  3. (1/4)MR^2 + (1/12)Mt^2

  4. (1/6)MR^2 + (1/12)Mt^2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The moment of inertia of a solid disk about an axis perpendicular to the disk and passing through its center is given by I = (1/2)MR^2 + (1/12)Mt^2.