A body is uniformly rotating about an axis fixed in an inertial frame of reference. Let \(\overrightarrow A\) be a unit vector along the axis of rotation and \(\overrightarrow B\) be the unit vector along the resultant force on a particle P of the body away from the axis. The value of \(\overrightarrow A.\overrightarrow B\) is:
1. 1
2. –1
3. 0
4. none of these
A particle moves with a constant velocity parallel to the X-axis. Its angular momentum with respect to the origin:
1. | is zero | 2. | remains constant |
3. | goes on increasing | 4. | goes on decreasing |
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:
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. | \(t\) and \(r\) | depends on the actual values of
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 |