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
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
A uniform cube of mass \(m\) and side \(a\) is placed on a frictionless horizontal surface. A vertical force \(F\) is applied to the edge as shown in the figure. Match the following (most appropriate choice).
| List- I | List- II | ||
| (a) | \(mg/4<F<mg/2\) | (i) | cube will move up. |
| (b) | \(F>mg/2\) | (ii) | cube will not exhibit motion. |
| (c) | \(F>mg\) | (iii) | cube will begin to rotate and slip at \(A\). |
| (d) | \(F=mg/4\) | (iv) | normal reaction effectively at \(a/3\) from \(A\), no motion. |
| 1. | a - (i), b - (iv), c - (ii), d - (iii) |
| 2. | a - (ii), b - (iii), c - (i), d - (iv) |
| 3. | a - (iii), b - (i), c - (ii), d - (iv) |
| 4. | a - (i), b - (ii), c - (iv), d - (iii) |
The figure shows a lamina in \(xy\text{-}\)plane. Two axes \({z}\) and \(z'\) pass perpendicular to its plane. A force \(\vec{F}\) acts in the plane of the lamina at point \(P\) as shown in the figure.
(The point \(P\) is closer to the \(z'\text-\)axis than the \(z\text{-}\)axis.)
| (a) | torque \(\vec{\tau}\)caused by \(\vec{F}\)about \(z\text{-}\)axis is along \((-\hat{k})\) |
| (b) | torque \(\vec{\tau}'\)caused by \(\vec{F}\)about \(z'\text-\)axis is along \((-\hat{k})\) |
| (c) | torque caused by \(\vec{F}\)about the \(z\text{-}\)axis is greater in magnitude than that about the \(z'\text-\)axis |
| (d) | total torque is given by \(\vec{\tau}_{net}=\vec{\tau}+\vec{\tau}'\) |
Choose the correct option from the given ones:
| 1. | (c) and (d) only |
| 2. | (a) and (c) only |
| 3. | (b) and (c) only |
| 4. | (a) and (b) only |
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