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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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 the centre-of-mass will be:
1. $$2v$$
2. zero
3. $$v$$
4. $$4v$$
Subtopic:  Center of Mass |
68%
From NCERT
NEET - 2023
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If $$\theta$$ is the angle between two vectors $\stackrel{\to }{\mathrm{a}}$ and $\stackrel{\to }{\mathrm{b}}$, and $|\stackrel{\to }{\mathrm{a}}×\stackrel{\to }{\mathrm{b}}|=\stackrel{\to }{\mathrm{a}}.\stackrel{\to }{\mathrm{b}}$, 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 |
68%
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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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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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