- 1(current)
Q. No.| 1. | \(200 ~\text{N}\) | 2. | \(200 \sqrt{3} ~\text{N}\) |
| 3. | \(100 ~\text{N}\) | 4. | \(100 \sqrt{3} ~\text{N}\) |
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 \(m\) is suspended from the rod at \(160~\text{cm}\) mark as shown in the figure. What would be the value of \(m\) such that the rod is in equilibrium?
(Take \(g=10~( \text {m/s}^2)\)
| 1. | \({\dfrac 1 6}~\text{kg}\) | 2. | \({\dfrac 1 {12}}~ \text{kg}\) |
| 3. | \({\dfrac 1 2}~ \text{kg}\) | 4. | \({\dfrac 1 3}~ \text{kg}\) |
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. | \(- 7 \hat{i} - 4 \hat{j} - 8 \hat{k}\) |
| 1. | \(wx \over d\) | 2. | \(wd \over x\) |
| 3. | \(w(d-x) \over x\) | 4. | \(w(d-x) \over d\) |
A rod \(PQ\) of mass \(M\) and length \(L\) is hinged at end \(P\). The rod is kept horizontal by a massless string tied to point \(Q\) as shown in the figure. When the string is cut, the initial angular acceleration of the rod is:
| 1. | \(\dfrac{g}{L}\) | 2. | \(\dfrac{2g}{L}\) |
| 3. | \(\dfrac{2g}{3L}\) | 4. | \(\dfrac{3g}{2L}\) |
\(\mathrm{ABC}\) is an equilateral triangle with \(O\) as its centre. \(F_1,\) \(F_2,\) and \(F_3\) represent three forces acting along the sides \({AB},\) \({BC}\) and \({AC}\) 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. | \(\dfrac{F_1+F_2}{2}\) | 4. | \(2F_1+F_2\) |
- 1(current)
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