NEET Physics: values of moments of inertia for simple geometrical objects Practice Questions
11 free multiple-choice questions on values of moments of inertia for simple geometrical objects (Rotational Motion) for NEET Physics, each with the correct answer and a step-by-step explanation. Attempt a question, then reveal the solution to check your reasoning.
Practice thousands more NEET questions in the app →Q1. A thin rod of mass M and length L is rotated about an axis perpendicular to the rod and passing through its center. What is the value of its moment of inertia?
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Correct answer: A — 1/12ML²
The moment of inertia of a thin rod rotating about its center is I = 1/12ML².
Q2. The moment of inertia of a solid sphere is I = 2/5MR². If the radius of the sphere is doubled, what will be the new moment of inertia?
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Correct answer: B — 16/5 MR²
The moment of inertia is proportional to R². If R is doubled (R' = 2R), the new moment of inertia I' = 2/5M(2R)² = 2/5M(4R²) = 4 (2/5MR²).
Q3. If the moment of inertia of a system of point masses is calculated, and the masses are distributed uniformly along a line, the moment of inertia is proportional to which factor?
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Correct answer: D — The square of the distance of the masses from the axis
For a system of point masses distributed along a line, the moment of inertia is I = Σmᵢ rᵢ². Since all masses are at the same distance r, I ∝ Σmᵢ, but if we consider the distribution, the squared distance is the critical factor.
Q4. If the moment of inertia of a sphere about an axis passing through its center is I, what is the moment of inertia of the same sphere about an axis passing through its center and perpendicular to a diameter?
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Correct answer: D — I
For a sphere, the moment of inertia is the same regardless of the axis passing through the center. (Note: This tests the conceptual property of symmetry, though usually I is expressed in terms of radius/mass).
Q5. The moment of inertia of a thin uniform hollow cylinder of mass M and radius R about an axis passing through its center and perpendicular to its length is given by which formula?
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Correct answer: B — MR²
For a thin uniform hollow cylinder rotating about an axis through its center perpendicular to its length, the moment of inertia is I = MR².
Q6. Which geometrical shape has the maximum moment of inertia for a given mass M and fixed extent?
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Correct answer: D — Solid disc
For a fixed mass distributed over a fixed volume or area, the moment of inertia is maximized when the mass is distributed as far away from the axis of rotation as possible. Among the standard shapes, a solid disc generally has a larger moment of inertia than a sphere or a rod of comparable dimensions, assuming rotation about a central axis.
Q7. A thin ring (hoop) of mass M and radius R is rotating about an axis passing through its center and perpendicular to its plane. What is the moment of inertia of the ring about this axis?
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Correct answer: D — MR²
For a thin ring rotating about an axis passing through its center and perpendicular to its plane, the moment of inertia is I = MR².
Q8. The moment of inertia of a hollow sphere of mass M and radius R about an axis passing through its center is given by:
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Correct answer: B — 2/3MR²
The moment of inertia (I) of a hollow sphere about an axis through its center is I = 2/3MR². This formula is derived by considering the mass distribution in a hollow spherical shell.
Q9. The moment of inertia of a uniform solid rod of mass M and length L about an axis passing through its center and perpendicular to the rod is:
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Correct answer: C — ML²/12
The moment of inertia of a rod about its center is I = 1/12ML².
Q10. The moment of inertia of a uniform thin ring (hoop) of mass M and radius R about its center is given by:
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Correct answer: D — MR
The moment of inertia of a ring about its center is I = MR².
Q11. A uniform solid disk of mass M and radius R rotates about an axis passing through its center. What is the moment of inertia of the disk about this axis?
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Correct answer: C — C1/2MR²
The moment of inertia of a uniform solid disk (or cylinder) of mass M and radius R about an axis passing through its center is given by the formula I = 1/2MR².
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