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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.  \({\dfrac 1 3}~ \text{kg}\)
Subtopic:  Torque |
 60%
Level 2: 60%+
NEET - 2021
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What would be the torque about the origin when a force \(3\hat{j}~\text N\) acts on a particle whose position vector is \(2\hat{k}~\text m?\)

1. \(6\hat{j}~\text{N-m}\)  2. \(-6\hat{i}~\text{N-m}\) 
3. \(6\hat{k}~\text{N-m}\)  4. \(6\hat{i}~\text{N-m}\)
Subtopic:  Torque |
 75%
Level 2: 60%+
NEET - 2020
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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. \(\dfrac{3g}{2L}\)
Subtopic:  Torque |
 82%
Level 1: 80%+
AIPMT - 2013
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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. \(w(d-x) \over d\)
Subtopic:  Torque |
 71%
Level 2: 60%+
NEET - 2015
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A force \(\vec F = \left(2 \hat{i} + 3 \hat{j} + 4 \hat{k} \right) \text{N}\) is acting at point \((2~\text{m}, -3~\text{m}, 6~\text{m}).\) Find the torque of this force about a point whose position vector is \(\left(2 \hat{i}+ 5\hat {j}+ 3\hat {k}\right) \text{m}\).
1. \(\vec{\tau}=(-17 \hat{\mathrm{i}}+6 \hat{\mathrm{j}}+4 \widehat{\mathrm{k}})\) N-m
2. \(\vec{\tau}=(-17 \hat{\mathrm{i}}+6 \hat{\mathrm{j}}-4 \widehat{\mathrm{k}}) \) N-m
3. \(\vec{\tau}=(17 \hat{\mathrm{i}}-6 \hat{\mathrm{j}}+4 \widehat{\mathrm{k}})\) N-m
4. \(\vec{\tau}=(-41 \hat{\mathrm{i}}+6 \hat{\mathrm{j}}+16 \hat{\mathrm{k}})\) N-m
Subtopic:  Torque |
 70%
Level 2: 60%+
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Four \(2~\text{kg}\) masses are connected by \(\dfrac{1}{4}~\text{m}\) spokes to an axle as in figure given below. A force \(F\) of \(24~\text{N}\) acts on a lever \(\dfrac{1}{2}~\text{m}\) long to produce an angular acceleration \(\mathit{\alpha}\). The magnitude of \(\mathit{\alpha}\) (in rad/s2) is:
     
1. \(2\) 2. \(12\)
3. \(6\) 4. \(3\)
Subtopic:  Torque |
 76%
Level 2: 60%+
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A \(\sqrt {34}\) m long ladder weighing \(10\) kg leans on a frictionless wall. Its feet rest on the floor \(3\) m away from the wall as shown in the figure. If \(\mathrm F_ \mathrm f\) and \(\mathrm F_ \mathrm w\) are the reaction forces of the floor and the wall, then ratio of \(\mathrm F_ \mathrm w / \mathrm F_ \mathrm f\) will be:  (Take \(g=10\) m/s2)
             
1. \(\dfrac{6}{\sqrt{110}} \)
2. \(\dfrac{3}{\sqrt{113}} \)
3. \(\dfrac{3}{\sqrt{109}} \)
4. \( \dfrac{2}{\sqrt{109}}\)
Subtopic:  Torque |
 67%
Level 2: 60%+
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Let \(\vec{F}\) be a force acting on a particle having position vector \(\vec{r}\). Let \(\vec{\tau}\) be the torque of this force about the origin, then:

1. \(\vec{r} \cdot \vec{\tau}=0\) and \(\vec{F} \cdot \vec{\tau}=0\)
2. \(\vec{r} \cdot \vec{\tau}=0\) but \(\vec{F} \cdot \vec{\tau} \neq 0\)
3. \(\vec{r} \cdot \vec{\tau} \neq 0\) but \(\vec{F} \cdot \vec{\tau}=0\)
4. \(\vec{r} \cdot \vec{\tau} \neq 0\) and \(\vec{F} \cdot \vec{\tau} \neq 0\)
Subtopic:  Torque |
 82%
Level 1: 80%+
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