NEET Physics: The moment of inertia Practice Questions

Correct answer: D — Rotational motion

The moment of inertia is the rotational analogue of mass; it measures an object's resistance to changes in its rotational motion.

Correct answer: C — Increase

Moment of inertia is proportional to the square of the distance from the axis of rotation. Increasing the distance increases the moment of inertia.

Correct answer: B — m₁ r₁² + m₂ r₂² + m₃ r₃²

The moment of inertia (I) of a system of discrete particles about an axis is defined as the sum of the products of the mass of each particle and the square of its perpendicular distance from the axis of rotation (I = Σm r²).

Correct answer: D — mr²

For a point mass (m) rotating at a perpendicular distance (r) from the axis, the moment of inertia is I = mr².

Correct answer: D — Moment of Inertia

Moment of Inertia (I) is a scalar quantity, as it depends only on the mass distribution relative to an axis, not on direction. Torque and Angular Momentum are vector quantities, and Angular Velocity is a vector.

Correct answer: C — I = m r²

The general definition for the moment of inertia of discrete particles about an axis is I = Σmᵢ rᵢ², where mᵢ is the mass and rᵢ is the perpendicular distance from the axis.

Correct answer: B — It is the mass of the body multiplied by its distance from the axis of rotation.

The moment of inertia (I) is defined as the rotational analog of mass. It quantifies the body's resistance to changes in its rotational motion (angular acceleration), and it is calculated as I = Σmᵢ rᵢ², where rᵢ is the perpendicular distance of mass mᵢ from the axis of rotation.

Correct answer: B — The sum of the squares of the distances of all masses from the axis

For discrete point masses, the moment of inertia about the center of mass is calculated as I₍CM) = Σmᵢ rᵢ², where rᵢ is the distance of mass mᵢ from the center of mass.

Correct answer: D — The sum of the squares of the masses

If all r are equal, I = Σm r² = r² Σm = r² M, where M is the total mass. Thus, I is directly proportional to the total mass (M).

Correct answer: D — MR

For a ring rotating about its center, the moment of inertia is I = MR².

Correct answer: C — Acceleration

Moment of inertia depends on the distribution of mass relative to the axis of rotation. While mass and density are related, acceleration is a kinematic quantity, and angular momentum relates to the rotational motion, not directly to the static moment of inertia calculation itself.

Correct answer: A — It is directly proportional to the total mass of the body.

The moment of inertia depends on both the mass distribution and the axis of rotation. It is not simply proportional to the total mass, nor is it independent of the axis of rotation.

Correct answer: D — I = Σm r²

The moment of inertia (I) of a system of discrete particles rotating about an axis is defined as the sum of the products of the mass of each particle and the square of its perpendicular distance (radius) from the axis of rotation (I = Σmᵢ rᵢ²).

Correct answer: B — Iₓ = I_y

The moment of inertia depends on the chosen axis of rotation. The relationship between Iₓ and I_y depends entirely on the geometry of the body and the location of the axes relative to the mass distribution. They are generally not equal unless the geometry is highly symmetric about the intersection point.