Q. No.A body is rotating uniformly about a vertical axis fixed in an inertial frame. The resultant force on a particle of the body not on the axis is:
1.
vertical
2.
horizontal and skew with the axis
3.
horizontal and intersecting the axis
4.
none of these
A body is rotating nonuniformly about a vertical axis fixed in an inertial frame. The resultant force on a particle of the body not on the axis is
1. vertical
2. horizontal and skew with the axis
3. horizontal and intersecting the axis
4. none of these
Let \(\vec{F}\) be a force acting on a particle having position vector \(\vec{r}\). Let \(\vec{\tau}\) be the torque of this force about the origin, then:
| 1. | \(\vec{r} \cdot \vec{\tau}=0\) and \(\vec{F} \cdot \vec{\tau}=0\) |
| 2. | \(\vec{r} \cdot \vec{\tau}=0\) but \(\vec{F} \cdot \vec{\tau} \neq 0\) |
| 3. | \(\vec{r} \cdot \vec{\tau} \neq 0\) but \(\vec{F} \cdot \vec{\tau}=0\) |
| 4. | \(\vec{r} \cdot \vec{\tau} \neq 0\) and \(\vec{F} \cdot \vec{\tau} \neq 0\) |
A uniform rod is kept vertically on a horizontal smooth surface at a point O. If it is rotated slightly and released, it falls down on the horizontal surface. The lower end will remain
1. at O
2. at a distance less than l/2 from O
3. at a distance l/2 from O
4. at a distance larger than l/2 from O
A circular disc A of radius \(r\) is made from an iron plate of thickness \(t\) and another circular disc B of radius \(4r\) is made from an iron plate of thickness \(t/4.\) The relation between the moments of inertia \(I_A\) and \(I_B\) is:
| 1. | \(I_A>I_B\) |
| 2. | \(I_A=I_B\) |
| 3. | \(I_A<I_B\) |
| 4. | depends on the actual values of \(t\) and \(r\) |
A circular disc A of radius r is made from an iron plate of thickness t and another circular disc B of radius 4r is made from an iron plate of thickness t/4. Equal torques act on discs A and B, initially both being at rest. At a later instant, the linear speeds of a point on the rim of A and another point on the rim of B are vA and vB respectively. We have
1. vA > vB
2. vA = vB
3. vA < vB
4. the relation depends on the actual magnitude of the torques
A closed cylindrical tube containing some water (not filling the entire tube) lies in a horizontal plane. If the tube is rotated about a perpendicular bisector, the moment of inertia of water about the axis:
| 1. | increases |
| 2. | decreases |
| 3. | remains constant |
| 4. | increases if the rotation is clockwise and decreases if it is anticlockwise |
The moment of inertia of a uniform semicircular wire of mass \(\mathrm{M}\) and radius \(\mathrm{r}\) about a line perpendicular to the plane of the wire through the centre is:
1. \(\mathrm{Mr}^{2}\)
2. \(\frac{1}{2} \mathrm{Mr}^{2}\)
3. \(\frac{1}{4} \mathrm{Mr}^{2}\)
4. \(\frac{2}{5} \mathrm{Mr}^{2}\)
Let \(I_1\) and \(I_2\) be the moments of inertia of two bodies of identical geometrical shape, the first made of aluminium and the second of iron:
| 1. | \(I_1 <I_2\) |
| 2. | \(I_1 = I_2\) |
| 3. | \(I_1>I_2\) |
| 4. | The relation between \(I_1\) and \(I_2\) depends on the actual shapes of the bodies |
A body having its centre of mass at the origin has three of its particles at (a, 0, 0), (0, a, 0), (0, 0, a). The moments of inertia of the body about the X and Y axes are 0.20 kg-m2 each. The moment of inertia about the Z-axis:
1. is 0.20 kg-m2
2. is 0.40 kg-m2
3. is \(0.20\sqrt2\) kg-m2
4. cannot be deduced with this information
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