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 |
 74%
From NCERT
To view explanation, please take trial in the course.
NEET 2021 - Achiever Batch - Aryan Raj Singh
Hints
Links
To view explanation, please take trial in the course.
NEET 2021 - Achiever Batch - Aryan Raj Singh

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 |
 61%
From NCERT
To view explanation, please take trial in the course.
NEET 2021 - Achiever Batch - Aryan Raj Singh
Hints
Links

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
Please attempt this question first.
Hints
Please attempt this question first.

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 |
 70%
From NCERT
NEET - 2023
Please attempt this question first.
Hints
Please attempt this question first.

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 |
 75%
From NCERT
To view explanation, please take trial in the course.
NEET 2021 - Achiever Batch - Aryan Raj Singh
Hints
Links

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 |
 59%
From NCERT
To view explanation, please take trial in the course.
NEET 2021 - Achiever Batch - Aryan Raj Singh
Hints
To view explanation, please take trial in the course.
NEET 2021 - Achiever Batch - Aryan Raj Singh

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
To view explanation, please take trial in the course.
NEET 2021 - Achiever Batch - Aryan Raj Singh
Hints
Links
To view explanation, please take trial in the course.
NEET 2021 - Achiever Batch - Aryan Raj Singh

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 |
 61%
From NCERT
To view explanation, please take trial in the course.
NEET 2021 - Achiever Batch - Aryan Raj Singh
Hints
Links
To view explanation, please take trial in the course.
NEET 2021 - Achiever Batch - Aryan Raj Singh

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
To view explanation, please take trial in the course.
NEET 2021 - Achiever Batch - Aryan Raj Singh
Hints
To view explanation, please take trial in the course.
NEET 2021 - Achiever Batch - Aryan Raj Singh

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
To view explanation, please take trial in the course.
NEET 2021 - Achiever Batch - Aryan Raj Singh
Hints
Links
To view explanation, please take trial in the course.
NEET 2021 - Achiever Batch - Aryan Raj Singh