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 are three forces acting along the sides AB, BC and AC. What should be the magnitude of so that total torque about O is zero?
1.
2.
3.
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, 8N at B, 6 N at C, and 9N 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) | \(a/3\) from A, no motion. | normal reaction effectively at
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. | \(295\) |
A uniform beam, \(3.0\) m long, of weight \(100\) N has a \(300\) N weight placed \(0.5\) m from one end. The beam is suspended by a string \(1.0\) m from the same end. A diagram of the weights placed on the beam is given below:
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 |