Q. No.A uniform rod of length \(200~ \text {cm}\) and mass \(500~ \text g\) is balanced on a wedge placed at \(40~ \text{cm}\) mark. A mass of \(2~\text{kg}\) is suspended from the rod at \(20~ \text{cm}\) and another unknown mass \( \text m\) is suspended from the rod at \(160~\text{cm}\) mark as shown in the figure. What would be the value of \( \mathrm{m}\) such that the rod is in equilibrium? (Take \(g=10~( \text {m/s}^2)\)
| 1. | \({1 \over 6}~ \text{kg}\) | 2. | \({1 \over 12}~ \text{kg}\) |
| 3. | \({1 \over 2}~ \text{kg}\) | 4. | \({1 \over 3}~ \text{kg}\) |
What would be the torque about the origin when a force \(3\hat{j}\) N acts on a particle whose position vector is \(2\hat{k}\) m?
1. \(6\hat{j}\) N-m
2. \(-6\hat{i}\) N-m
3. \(6\hat{k}\) N-m
4. \(6\hat{i}\) N-m
A solid cylinder of mass \(2\) kg and radius \(4\) cm is rotating about its axis at the rate of \(3\) rpm. The torque required to stop after \(2\pi\) revolutions is:
1. \(2\times 10^6\) N-m
2. \(2\times 10^{-6}\) N-m
3. \(2\times 10^{-3}\) N-m
4. \(12\times 10^{-4}\) N-m
The moment of the force, \(\overset{\rightarrow}{F} = 4 \hat{i} + 5 \hat{j} - 6 \hat{k}\) at point (\(2,\) \(0,\) \(-3\)) about the point (\(2,\) \(-2,\) \(-2\)) is given by:
1. \(- 8 \hat{i} - 4 \hat{j} - 7 \hat{k}\)
2. \(- 4 \hat{i} - \hat{j} - 8 \hat{k}\)
3. \(- 7 \hat{i} - 8 \hat{j} - 4 \hat{k}\)
4. \(- 7 \hat{i} - 4 \hat{j} - 8 \hat{k}\)
A rod of weight \(w\) is supported by two parallel knife edges, A and B, and is in equilibrium in a horizontal position. The knives are at a distance \(d\) from each other. The centre of mass of the rod is at a distance \(x \) from A. The normal reaction on A is:
| 1. | \(wx \over d\) | 2. | \(wd \over x\) |
| 3. | \(w(d-x) \over x\) | 4. | \(w(d-x) \over d\) |
An automobile moves on a road with a speed of \(54~\text{kmh}^{-1}.\) The radius of its wheels is \(0.45\) m and the moment of inertia of the wheel about its axis of rotation is \(3~\text{kg-m}^2.\) If the vehicle is brought to rest in \(15\) s, the magnitude of average torque transmitted by its brakes to the wheel is:
1. \(6.66~\text{kg-m}^2\text{s}^{-2}\)
2. \(8.58~\text{kg-m}^2\text{s}^{-2}\)
3. \(10.86~\text{kg-m}^2\text{s}^{-2}\)
4. \(2.86~\text{kg-m}^2\text{s}^{-2}\)
A rod \(\mathrm{PQ}\) of mass \(M\) and length \(L\) is hinged at end \(\mathrm{P}\). The rod is kept horizontal by a massless string tied to point \(\mathrm{Q}\) as shown in the figure. When the string is cut, the initial angular acceleration of the rod is:
1. \(\frac{g}{L}\)
2. \(\frac{2g}{L}\)
3. \(\frac{2g}{3L}\)
4. \(\frac{3g}{2L}\)
\(\mathrm{ABC}\) is an equilateral triangle with \(O\) as its centre. \(F_1\), \(F_2\), and \(F_3\) represent three forces acting along the sides \(\mathrm{AB},\) \(\mathrm{BC}\) and \(\mathrm{AC}\) respectively. If the total torque about \(O\) is zero, then the magnitude of \(F_3\) is:
1. \(F_1+F_2\)
2. \(F_1-F_2\)
3. \(\frac{F_1+F_2}{2}\)
4. \(2F_1+F_2\)
If \(\vec F\) is the force acting on a particle having position vector \(\vec r\) and \(\vec \tau\) be the torque of this force about the origin, then:
| 1. | \(\vec r\cdot\vec \tau\neq0\text{ and }\vec F\cdot\vec \tau=0\) |
| 2. | \(\vec r\cdot\vec \tau>0\text{ and }\vec F\cdot\vec \tau<0\) |
| 3. | \(\vec r\cdot\vec \tau=0\text{ and }\vec F\cdot\vec \tau=0\) |
| 4. | \(\vec r\cdot\vec \tau=0\text{ and }\vec F\cdot\vec \tau\neq0\) |
A uniform rod of length \(l\) and mass \(M\) is free to rotate in a vertical plane about \(A\). The rod, initially in the horizontal position, is released. The initial angular acceleration of the rod is: (Moment of inertia of the rod about \(A\) is \(\frac{Ml^2}{3}\))
1. \(\frac{3g}{2l}\)
2. \(\frac{2l}{3g}\)
3. \(\frac{3g}{2l^2}\)
4. \(\frac{Mg}{2}\)
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