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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: Moment of Inertia |
Level 3: 35%-60%
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The angular speed of a flywheel is increased from \(600\) rpm to \(1200\) rpm in \(10\) s. The number of revolutions completed by the flywheel during this time is:
1. \(600\)
2. \(900\)
3. \(300\)
4. \(150\)
1. \(600\)
2. \(900\)
3. \(300\)
4. \(150\)
Subtopic: Rotational Motion: Kinematics |
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A thin horizontal disc is rotating about a vertical axis passing through its fixed centre \(O.\) Its angular momentum is \(L_A\) and \(L_B\) computed about points \(A\) and \(B,\) respectively, with \(OB =2 \times OA.\) The value of \(\dfrac{L_A}{L_B}\) is:
| 1. | \(2\) | 2. | \(\dfrac{1}{4}\) |
| 3. | \(\dfrac{1}{2}\) | 4. | \(1\) |
Subtopic: Angular Momentum |
Level 4: Below 35%
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A frictionless circular wire of unit radius is fixed on the horizontal plane. Two-point particles of unit mass start moving simultaneously from point \(A(0 =\dfrac{\pi}{2})\) with identical uniform angular speeds in opposite directions and meet again at point \(B(0 =-\dfrac{\pi}{2})\). During this time, which of the following graphs schematically represents the magnitude of the total linear momentum \(P\) of the system as a function of \(\theta?\)
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: Linear Momentum |
Level 3: 35%-60%
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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: Moment of Inertia |
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A uniform rod of mass \(20~\text{kg}\) and length \(5\text{ m}\) leans against a smooth vertical wall making an angle of \(60^{\circ}\) with it. The other end rests on a rough horizontal floor. The friction force that the floor exerts on the rod is: (take \(g=10~\text{m/s}^2\) )
| 1. | \(200 ~\text{N}\) | 2. | \(200 \sqrt{3} ~\text{N}\) |
| 3. | \(100 ~\text{N}\) | 4. | \(100 \sqrt{3} ~\text{N}\) |
Subtopic: Torque |
Level 3: 35%-60%
NEET - 2025
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The sun rotates around its centre once in \(27\) days. What will be the period of revolution if the sun were to expand to twice its present radius without any external influence? Assume the sun to be a sphere of uniform density.
| 1. | \(115\) days | 2. | \(108\) days |
| 3. | \(100\) days | 4. | \(105\) days |
Subtopic: Angular Momentum |
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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: Moment of Inertia |
Level 3: 35%-60%
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A wheel of a bullock cart is rolling on a level road as shown in the figure below. If its linear speed is \(v\) in the direction shown, which one of the following options is correct (\(P\) and \(Q\) are any highest and lowest points on the wheel, respectively)?
| 1. | Point \(P\) moves faster than point \(Q\). |
| 2. | Both the points \(P\) and \(Q\) move with equal speed. |
| 3. | Point \(P\) has zero speed. |
| 4. | Point \(P\) moves slower than point \(Q\). |
55%
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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: Moment of Inertia |
62%
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