Q. No.The angular speed of the wheel of a vehicle is increased from \(360~\text{rpm}\) to \(1200~\text{rpm}\) in \(14\) seconds. Its angular acceleration will be:
1. \(2\pi ~\text{rad/s}^2\)
2. \(28\pi ~\text{rad/s}^2\)
3. \(120\pi ~\text{rad/s}^2\)
4. \(1 ~\text{rad/s}^2\)
1. \(2\pi ~\text{rad/s}^2\)
2. \(28\pi ~\text{rad/s}^2\)
3. \(120\pi ~\text{rad/s}^2\)
4. \(1 ~\text{rad/s}^2\)
Given the following statements:
| (a) | The centre of gravity (C.G.) of a body is the point at which the weight of the body acts. |
| (b) | If the earth is assumed to have an infinitely large radius, the centre of mass coincides with the centre of gravity. |
| (c) | To evaluate the gravitational field intensity due to any body at an external point, the entire mass of the body can be considered to be concentrated at its C.G. |
| (d) | The radius of gyration of any body rotating about an axis is the length of the perpendicular dropped from the C.G. of the body to the axis. |
Which one of the following pairs of statements is correct?
| 1. | (a) and (b) | 2. | (b) and (c) |
| 3. | (c) and (d) | 4. | (d) and (a) |
In the figure given below, \(O\) is the centre of an equilateral triangle \(ABC\) and \(\vec{F_{1}} ,\vec F_{2}, \vec F_{3}\) are three forces acting along the sides \(AB\), \(BC\) and \(AC\). What should be the magnitude of \(\vec{F_{3}}\) so that total torque about \(O\) is zero?
1. \(\left|\vec{F_{3}}\right|= \left|\vec{F_{1}}\right|+\left|\vec{F_{2}}\right|\)
2. \(\left|\vec{F_{3}}\right|= \left|\vec{F_{1}}\right|-\left|\vec{F_{2}}\right|\)
3. \(\left|\vec{F_{3}}\right|= \vec{F_{1}}+2\vec{F_{2}}\)
4. Not possible
The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the
plane of the ring will be:
1. \(2:1\)
2. :
3. \(2:3\)
4. \(1:\)
A circular disc is to be made by using iron and aluminium so that it acquires a maximum moment of inertia about its geometrical axis. It is possible with:
| 1. | Aluminium in the interior and iron surrounding it |
| 2. | Iron at the interior and aluminium surrounding it |
| 3. | Using iron and aluminium layers in alternate order |
| 4. | A sheet of iron is used at both the external surface and aluminium sheet as the internal layer |
For a body, with angular velocity \( \vec{\omega }=\hat{i}-2\hat{j}+3\hat{k}\) and radius vector \( \vec{r }=\hat{i}+\hat{j}++\hat{k},\) its velocity will be:
1. \(-5\hat{i}+2\hat{j}+3\hat{k}\)
2. \(-5\hat{i}+2\hat{j}-3\hat{k}\)
3. \(-5\hat{i}-2\hat{j}+3\hat{k}\)
4. \(-5\hat{i}-2\hat{j}-3\hat{k}\)
| 1. | \(1.5\) m | 2. | \(2\) m |
| 3. | \(2.5\) m | 4. | \(3.0\) m |
A wheel has an angular acceleration of \(3.0~\text{rad/s}^2\) and an initial angular speed of \(2.00~\text{rad/s}.\) In a time of \(2~\text s,\) it has rotated through an angle (in radians) of:
1. \(6\)
2. \(10\)
3. \(12\)
4. \(4\)
Two gear wheels that are meshed together have radii of \(0.50\) cm and \(0.15\) cm. The number of revolutions made by the smaller one when the larger one goes through \(3\) revolutions is:
1. \(5\) revolutions
2. \(20\) revolutions
3. \(1\) revolution
4. \(10\) revolutions
From a circular ring of mass \({M}\) and radius \(R,\) an arc corresponding to a \(90^\circ\) sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is \(K\) times \(MR^2.\) The value of \(K\) will be:
| 1. | \(\frac{1}{4}\) | 2. | \(\frac{1}{8}\) |
| 3. | \(\frac{3}{4}\) | 4. | \(\frac{7}{8}\) |
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