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 |
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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 the centre-of-mass will be:
1. \(2v\)
2. zero
3. \(v\)
4. \(4v\)
Subtopic:  Center of Mass |
 69%
From NCERT
NEET - 2023
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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 |
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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 \(w=\dfrac{v}{r}\). Thus:
1. \(w\propto\dfrac{1}{r}\)
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 |
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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 |
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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 \({\dfrac g 4}\) (\(g\): 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. \({\dfrac b 2}\) 2. \({ \dfrac b 4}\) 
3. \({\dfrac b 8}\) 4. \(\dfrac b 3\)
Subtopic:  Torque |
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A particle of mass \(m\) moves in the XY plane with a velocity \(v\) along the straight line AB. If the angular momentum of the particle with respect to the origin \(O\) is \(L_A\) when it is at \(A\) and \(L_B\) when it is at \(B,\) then: 
         

1. \(L_A>L_B\)
2. \(L_A=L_B\)
3. the relationship between \(L_A\) and \(L_B\) depends upon the slope of the line \(AB.\)
4. \(L_A<L_B\)
Subtopic:  Angular Momentum |
 69%
From NCERT
AIPMT - 2007
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