A body is in pure rotation. The linear speed \(v\) of a particle, the distance \(r\) of the particle from the axis and the angular velocity \(\omega\) of the body are related as \(w=\dfrac{v}{r}\). Thus:
1. \(w\propto\dfrac{1}{r}\)
2. \(w\propto\ r\)
3. \(w=0\)
4. \(w\) is independent of \(r\)

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:

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:

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:

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 v_A and v_B respectively. We have

1. v_A > v_B

2. v_A = v_B

3. v_A < v_B

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:

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: