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Q. No.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 |
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Level 3: 35%-60%
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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
1. \(115\) days
2. \(108\) days
3. \(100\) days
4. \(105\) days
Subtopic: Angular Momentum |
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Level 2: 60%+
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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 \(Q\). |
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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 |
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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:
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| \((A)\) | \((B)\) |
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| \((C)\) | \((D)\) |
| 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: Moment of Inertia |
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A body of mass \(6~\text{kg}\) is moving from its initial position \(A\) to the next position \(B\) as shown in the figure. From \(A\) to \(B\), the value of the momentum of the body is (in SI units):
| 1. | \(24\) | 2. | \(12\) |
| 3. | \(8\) | 4. | \(6\) |
Subtopic: Linear Momentum |
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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: Moment of Inertia |
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Let \(\omega_{1},\omega_{2}\) and \(\omega_{3}\) be the angular speeds of the second hand, minute hand, and hour hand of a smoothly running analog clock, respectively. If \(x_{1},x_{2}\) and \(x_{3}\) are their respective angular distance in \(1~\text{minute},\) then the factor that remains constant \((k)\) is:
| 1. | \(\dfrac{\omega_1}{x_1}=\dfrac{\omega_2}{x_2}=\dfrac{\omega_3}{x_3}={k}\) |
| 2. | \(\omega_{1}x_{1}=\omega_{2}x_{2}=\omega_{3}x_{3}={k}\) |
| 3. | \(\omega_{1}x_{1}^{2}=\omega_{2}x_{2}^{2}=\omega_{3}x_{3}^{2}={k}\) |
| 4. | \(\omega_{1}^{2}x_{1}=\omega_{2}^{2}x_{2}=\omega_{3}^{2}x_{3}={k}\) |
Subtopic: Rotational Motion: Kinematics |
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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: Moment of Inertia |
68%
Level 2: 60%+
NEET - 2023
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