Q. No.1. \(-\frac{\pi}{100} \) N-m
2. \(-\frac{\pi}{50} \) N-m
3. \(-\frac{\pi}{20} \) N-m
4. \(-\frac{\pi}{10}\) N-m
To maintain a rotor at a uniform angular speed of \(200\) rad s–1, an engine needs to transmit a torque of \(180\) N-m. What is the power required by the engine?
| 1. | \(33\) kW | 2. | \(36\) kW |
| 3. | \(28\) kW | 4. | \(76\) kW |
The value of \(M\), as shown, for which the rod will be in equilibrium is:
| 1. | \(1\) kg | 2. | \(2\) kg |
| 3. | \(4\) kg | 4. | \(6\) kg |
A rope of negligible mass is wound around a hollow cylinder of mass \(3\) kg and radius \(40\) cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of \(30\) N?
(Assume that there is no slipping.)
1. \(21\) rad/s2
2. \(24\) rad/s2
3. \(20\) rad/s2
4. \(25\) rad/s2
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 wheel with a radius of \(20\) cm has forces applied to it as shown in the figure. The torque produced by the forces of \(4\) N at \(A\), \(8~\)N at \(B\), \(6\) N at \(C\), and \(9~\)N at \(D\), at the angles indicated, is:
1. \(5.4\) N-m anticlockwise
2. \(1.80\) N-m clockwise
3. \(2.0\) N-m clockwise
4. \(3.6\) N-m clockwise
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) |
Which of the following is the value of the torque of force \(F\) about origin \(O:\)
1. \(\vec{\tau}=5(1-\sqrt{3}) \hat{k}\) N-m
2. \(\vec{\tau}=5(1-\sqrt{3}) \hat{j}\) N-m
3. \(\vec{\tau}=5(\sqrt{3}-1) \hat{i}\) N-m
4. \(\vec{\tau}=\sqrt{3} \hat{j}\) N-m
A force \(\vec{F}=\hat{i}+2\hat{j}+3\hat{k}~\text{N}\) acts at a point \(\hat{4i}+3\hat{j}-\hat{k}~\text{m}\). Let the magnitude of the torque about the point \(\hat{i}+2\hat{j}+\hat{k}~\text{m}\) be \(\sqrt{x}~\text{N-m}\). The value of \(x\) is:
| 1. | \(145\) | 2. | \(195\) |
| 3. | \(245\) | 4. | \(295\) |
How far from the other end must a weight of \(80\) N be placed for the beam to be balanced?
| 1. | \(0.75\) m | 2. | \(2.25\) m |
| 3. | \(1.25\) m | 4. | \(1.875\) m |
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