Q. No.A thin wire of length '\(L\)' and linear mass density '\(m\)' is bent into a circular ring (in \(x\text-y\) plane) with centre '\(C\)' as shown in figure. The moment of inertia of the ring about an axis \(yy'\) will be:
| 1. | \(\dfrac{3 {~mL}^3}{8 \pi^2} \) | 2. | \(\dfrac{3 {mL}^3}{8 \pi} \) |
| 3. | \(\dfrac{3 {mL}^2}{8 \pi^2} \) | 4. | \(\dfrac{3{mL}^2}{8 \pi}\) |
Subtopic: Â Moment of Inertia |
Level 3: 35%-60%
NEET - 2026
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A solid sphere \(A\) of radius \(R\) and mass \(M\) is attached at a point to a smaller solid sphere \(B\) of radius \(r<R\) and mass \(m<M.\) Assume that the line joining their centres lies along the horizontal. The moment of inertia of the system calculated about a vertical axis passing through the centre of \(A\) is \(I_A\) and that calculated about a vertical axis passing through the centre of \(B\) is \(I_B.\) The difference \(I_A-I_B\) is:
1. \(0\)
2. \((M-m)(R+r)^2\)
3. \((m-M)(R+r)^2\)
4. \((m-M)(R-r)^2\)
1. \(0\)
2. \((M-m)(R+r)^2\)
3. \((m-M)(R+r)^2\)
4. \((m-M)(R-r)^2\)
Subtopic: Â Moment of Inertia |
Level 3: 35%-60%
NEET - 2026
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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:
| 1. | \(\dfrac{7}{57}\) | 2. | \(\dfrac{7}{64}\) |
| 3. | \(\dfrac{7}{8}\) | 4. | \(\dfrac{7}{40}\) |
Subtopic: Â Moment of Inertia |
Level 3: 35%-60%
NEET - 2025
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The moment of inertia of a thin rod about an axis passing through its mid-point and perpendicular to the rod is \(2400 ~\text{g cm}^2.\) The length of the \(400~\text{g}\) rod is nearly:
1. \(17.5~\text{cm}\)
2. \(20.7~\text{cm}\)
3. \(72.0~\text{cm}\)
4. \(8.5~\text{cm}\)
1. \(17.5~\text{cm}\)
2. \(20.7~\text{cm}\)
3. \(72.0~\text{cm}\)
4. \(8.5~\text{cm}\)
Subtopic: Â Moment of Inertia |
 62%
Level 2: 60%+
NEET - 2024
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Consider a thin circular ring \((A),\) a circular disc \((B),\) a hollow cylinder \((C)\) and a solid cylinder \((D)\) of the same radii \(R\) and of the same masses.
If \(I_A, I_B, I_C \) and \(I_D\) are their moments of inertia about the axis shown, then choose the correct answer from the options given below:
 |
 |
| \((A)\) | \((B)\) |
 |
 |
| \((C)\) | \((D)\) |
| 1. | \({I}_A={I}_C~ \text{and} ~2{I}_B={I}_D\) |
| 2. | \(I_A=2 I_B~ \text{and} ~2 I_C=I_D \) |
| 3. | \(2 I_A=I_C~ \text{and} ~I_B=2 I_D\) |
| 4. | \({I}_{{A}}={I}_B={I}_C=2 {I}_{{D}}\) |
Subtopic: Â Moment of Inertia |
 66%
Level 2: 60%+
NEET - 2024
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The radius of gyration of a solid sphere of mass \(5~\text{kg}\) about \(XY \text- \text{axis}\) is \(5~\text m\) as shown in the figure. If the radius of the sphere is \(\frac{5x}{\sqrt{7}}~\text m,\) then the value of \(x\) is:
| 1. | \(5\) | 2. | \(\sqrt{2}\) |
| 3. | \(\sqrt{3}\) | 4. | \(\sqrt{5}\) |
Subtopic: Â Moment of Inertia |
 73%
Level 2: 60%+
NEET - 2024
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The ratio of the radius of gyration of a solid sphere of mass \(M\) and radius \(R\) about its own axis to the radius of gyration of the thin hollow sphere of the same mass and radius about its axis is:
1. \(5:2\)
2. \(3:5\)
3. \(5:3\)
4. \(2:5\)
1. \(5:2\)
2. \(3:5\)
3. \(5:3\)
4. \(2:5\)
Subtopic: Â Moment of Inertia |
 70%
Level 2: 60%+
NEET - 2023
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The ratio of the radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is:
| 1. | \(1:\sqrt{2}\) | 2. | \(2:1\) |
| 3. | \(\sqrt{2}:1\) | 4. | \(4:1\) |
Subtopic: Â Moment of Inertia |
 68%
Level 2: 60%+
NEET - 2022
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The ratio of the moments of inertia of two spheres, about their diameters, having the same mass and their radii being in the ratio of \(1:2\), is:
| 1. | \(2:1\) | 2. | \(4:1\) |
| 3. | \(1:2\) | 4. | \(1:4\) |
Subtopic: Â Moment of Inertia |
 82%
Level 1: 80%+
NEET - 2022
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An energy of \(484~\text J\) is spent in increasing the speed of a flywheel from \(60~\text{rpm}\) to \(360~\text{rpm}.\) The moment of inertia of the flywheel is:
| 1. | \(0.7~\text{kg-m}^2\) | 2. | \(3.22~\text{kg-m}^2\) |
| 3. | \(30.8~\text{kg-m}^2\) | 4. | \(0.07~\text{kg-m}^2\) |
Subtopic: Â Moment of Inertia |
 59%
Level 3: 35%-60%
NEET - 2022
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