Q. No.One solid sphere A and another hollow sphere B are of same mass and same outer radii. Their moment of inertia about their diameters are respectively \(\text{I}_{A}\) and \(\text{I}_{B}\) such that
1. \(\text{I}_{\text{A}}=\text{I}_{\text{B}}\)
2. \(\text{I}_{\text{A}}>\text{I}_{\text{B}}\)
3. \(\text{I}_{\text{A}}<\text{I}_{\text{B}}\)
4. \(\frac{\text{I}_{\text{A}}}{\text{I}_{\text{B}}}=\frac{d_A}{d_B}\)
1. \(\text{I}_{\text{A}}=\text{I}_{\text{B}}\)
2. \(\text{I}_{\text{A}}>\text{I}_{\text{B}}\)
3. \(\text{I}_{\text{A}}<\text{I}_{\text{B}}\)
4. \(\frac{\text{I}_{\text{A}}}{\text{I}_{\text{B}}}=\frac{d_A}{d_B}\)
A particle of mass \(1 ~\text{kg}\) is kept at (1m, 1m, 1m). \((1~\text{m},~1~\text{m},~1~\text{m}),\) The moment of inertia of this particle about \(z-\)axis would be
1. \(1~\text{kg}-\text{m}^2\)
2. \(2~\text{kg}-\text{m}^2\)
3. \(3~\text{kg}-\text{m}^2\)
4. None of these
A horizontal platform is rotating with uniform angular velocity around the vertical axis passing through its centre. At some instant of time a viscous fluid of mass 'm' is dropped at the centre and is allowed to spread out and finally fall. The angular velocity during this period
1. Decreases continuously
2. Decreases initially and increases again
3. Remains unaltered
4. Increases continuously
For \(L = 3.0~\text{m,}\) the total torque about pivot A provided by the forces as shown in the figure is:
| 1. | \(210 ~\text{Nm}\) | 2. | \(140 ~\text{Nm}\) |
| 3. | \(95 ~\text{Nm}\) | 4. | \(75 ~\text{Nm}\) |
For the same total mass, which of the following will have the largest moment of inertia about an axis passing through the centre of gravity and perpendicular to the plane of the body?
1. A disc of radius \(a\)
2. a ring of radius \(a\)
3. a square lamina of side \(2a\)
4. four rods forming square of side \(2a\)
The radius of gyration of a uniform rod of length \(L\) about an axis passing through its centre of mass is
1. \(\frac{L}{2 \sqrt{3}}\)
2. \(\frac{L^2}{12}\)
3. \(\frac{L}{\sqrt{3}}\)
4. \(\frac{L}{\sqrt{2}}\)
1. \(\frac{Ml^2}{12}\)
2. \(\frac{Ml^2}{6}\)
3. \(\frac{Ml^2}{4}\)
4. \(\frac{Ml^2}{3}\)
1. \(50\%\)
2. \(100\%\)
3. \(125\%\)
4. \(25\%\)
A solid sphere, a hollow sphere, and a disc, all having the same mass and radius, are placed at the top of a smooth incline and released. Least time will be taken in reaching the bottom by
| 1. | the solid sphere |
| 2. | the hollow sphere |
| 3. | the disc |
| 4. | all will take the same time |
If the kinetic energy of a body increases by \(0.1\%,\) the percent increase of its momentum will be
1. \(0.05\%\)
2. \(0.1\%\)
3. \(1.0\%\)
4. \(10\%\)
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