Which of the following points is the likely position of the center of mass of the system shown in the figure?

 

1. \(A\)
2. \(B\)
3. \(C\)
4. \(D\)

Subtopic:  Center of Mass |
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In the \(\mathrm{HCl}\) molecule, the separation between the nuclei of the two atoms is about \(1.27~\mathring{\text A}~(1~\mathring{\text A}=10^{10}~\text m).\) Then the approximate location of the CM of the molecule is:
(Given that a chlorine atom is about \(35.5\) times as massive as a hydrogen atom and nearly all the mass of an atom is concentrated in its nucleus).

1. \(1.235~\mathring{\text A}\) from \(\mathrm{H-}\)atom
2. \(2.41~\mathring{\text A}\) from \(\mathrm{Cl-}\)atom
3. \(3.40~\mathring{\text A}\) from \(\mathrm{Cl-}\)atom
4. \(1.07~\mathring{\text A}\) from \(\mathrm{H-}\)atom
Subtopic:  Center of Mass |
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Two blocks are joined by a light spring of spring constant, \(k=1000\) N/m, and are placed at rest on a horizontal frictionless table. A horizontal force of \(6\) N acts on the \(2\) kg block. The acceleration of the centre-of-mass of the system is:
                
1. \(3\) m/s2
2. \(2\) m/s2
3. \(1.5\) m/s2
4. \(4.5\) m/s2
Subtopic:  Center of Mass |
 73%
From NCERT
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Two particles \(A\) and \(B\) initially at rest, move towards each other under mutual force of attraction. At an instance when the speed of \(A\) is \(v\) and speed of \(B\) is \(3v\), the speed of center of mass is:
1. \(2v\) 2. zero
3. \(v\) 4. \(4v\)
Subtopic:  Center of Mass |
 69%
From NCERT
NEET - 2023
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If \(\theta\) is the angle between two vectors a and b, and |a×b|=a.b, then \(\theta\) is equal to:
1. \(0^\circ\)
2. \(180^\circ\)
3. \(135^\circ\)
4. \(45^\circ\)

Subtopic:  Vector Product |
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A vector \(\overrightarrow A\) points vertically upward and \(\overrightarrow B\) points towards north. The vector product \(\overrightarrow A\times\overrightarrow B\) is:

1. along west 2. along east
3. zero 4. vertically downward
Subtopic:  Vector Product |
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For a body, with angular velocity \( \vec{\omega }=\hat{i}-2\hat{j}+3\hat{k}\)  and radius vector \( \vec{r }=\hat{i}+\hat{j}++\hat{k},\)  its velocity will be:
1. \(-5\hat{i}+2\hat{j}+3\hat{k}\)
2. \(-5\hat{i}+2\hat{j}-3\hat{k}\)
3. \(-5\hat{i}-2\hat{j}+3\hat{k}\)
4. \(-5\hat{i}-2\hat{j}-3\hat{k}\)

Subtopic:  Rotational Motion: Kinematics |
 69%
From NCERT
AIPMT - 1999
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A body is in pure rotation. The linear speed \(v\) of a particle, the distance \(r\) of the particle from the axis and the angular velocity \(\omega\) of the body are related as \(w=\frac{v}{r}\). Thus:
1. \(w\propto\frac{1}{r}\)
2. \(w\propto\ r\)
3. \(w=0\)
4. \(w\) is independent of \(r\)

Subtopic:  Rotational Motion: Kinematics |
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The angular speed of a flywheel moving with uniform angular acceleration changes from \(1200\) rpm to \(3120\) rpm in \(16\) s. The angular acceleration in rad/s² is:
1. \(104 \pi\)
2. \(2\pi\)
3. \(4\pi\)
4. \(12\pi\)
Subtopic:  Rotational Motion: Kinematics |
 73%
From NCERT
NEET - 2022
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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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