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. \(\vec r\cdot\vec \tau=0\text{ and }\vec F\cdot\vec \tau\neq0\)
Subtopic:  Torque |
 82%
From NCERT
AIPMT - 2009
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A block \(A\) is pushed on a smooth horizontal plane by applying a horizontal force \(F ,\) which causes an acceleration of \({g \over 4}\) (\(g\): acceleration due to gravity). The block does not topple, even though the force acts at its highest point. The normal reaction shifts forward by:
               
1. \({ b\over 2}\)
2. \({ b\over 4}\) 
3. \({ b\over 8}\)
4. \(b\over 3\)
Subtopic:  Torque |
From NCERT
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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 \( \text m\) is suspended from the rod at \(160~\text{cm}\) mark as shown in the figure. What would be the value of \(\text m\) 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.  \({1 \over 3}~ \text{kg}\)
Subtopic:  Torque |
 53%
From NCERT
NEET - 2021
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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 |
 66%
From NCERT
NEET - 2015
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A non-uniform bar of weight \(W\) is suspended at rest by two strings of negligible weight as shown in the figure. The angles made by the strings with the vertical are \(36.9^\circ\) and  \(53.1^\circ\) respectively. The bar is \(2\) m long. The distance \(d\) of the center of gravity of the bar from its left end is:
(Take sin\(36.9^\circ=0.6\) and sin\(53.1^\circ=0.8\))

           
1. \(69\) cm
2. \(72\) cm
3. \(79\) cm
4. \(65\) cm

Subtopic:  Torque |
 58%
From NCERT
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A uniform ladder of mass \(10\) kg is placed at an angle against a frictionless vertical wall, as shown in the figure, by applying a horizontal force \(F\) at the bottom \((B)\) of the ladder, towards the wall. (Take \(g=10\) m/s2).
             
The normal reaction of the ground on the ladder is:
1. \(100\) N
2. \(100\sqrt3\) N
3. \(50\) N
5. \(50\sqrt3\) N
Subtopic:  Torque |
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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

Subtopic:  Torque |
 88%
From NCERT
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