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. | \({\dfrac 1 3}~ \text{kg}\) |
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NEET MCQ Books for XIth & XIIth Physics, Chemistry & BiologyWhat 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 |
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NEET MCQ Books for XIth & XIIth Physics, Chemistry & BiologyA 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
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NEET MCQ Books for XIth & XIIth Physics, Chemistry & BiologyThe 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. \(- 7 \hat{i} - 4 \hat{j} - 8 \hat{k}\)
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NEET MCQ Books for XIth & XIIth Physics, Chemistry & Biology1. | \(wx \over d\) | 2. | \(wd \over x\) |
3. | \(w(d-x) \over x\) | 4. | \(w(d-x) \over d\) |
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NEET MCQ Books for XIth & XIIth Physics, Chemistry & BiologyAn 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. \(2.86~\text{kg-m}^2\text{s}^{-2}\)
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NEET MCQ Books for XIth & XIIth Physics, Chemistry & BiologyA 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. \(\frac{3g}{2L}\)
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NEET MCQ Books for XIth & XIIth Physics, Chemistry & Biology\(\mathrm{ABC}\) 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. \(2F_1+F_2\)
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NEET MCQ Books for XIth & XIIth Physics, Chemistry & BiologyIf \(\vec F\) 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. | \(\vec r\cdot\vec \tau=0\text{ and }\vec F\cdot\vec \tau\neq0\) |
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NEET MCQ Books for XIth & XIIth Physics, Chemistry & BiologyA 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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NEET MCQ Books for XIth & XIIth Physics, Chemistry & Biology