What would be the torque about the origin when a force \(3\hat{j}\) N acts on a particle whose position vector is \(2\hat{k}\) m?
1. \(6\hat{j}\) N-m
2. \(-6\hat{i}\) N-m
3. \(6\hat{k}\) N-m
4. \(6\hat{i}\) N-m

Subtopic:  Torque |
 73%
From NCERT
NEET - 2020
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Two particles of mass \(5~\text{kg}\) and \(10~\text{kg}\) respectively are attached to the two ends of a rigid rod of length \(1~\text{m}\) with negligible mass. The centre of mass of the system from the \(5~\text{kg}\) particle is nearly at a distance of:
1. \(50~\text{cm}\)
2. \(67~\text{cm}\)
3. \(80~\text{cm}\)
4. \(33~\text{cm}\)

Subtopic:  Center of Mass |
 80%
From NCERT
NEET - 2020
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The angular speed of the wheel of a vehicle is increased from \(360~\text{rpm}\) to \(1200~\text{rpm}\) in \(14\) seconds. Its angular acceleration will be:

1. \(2\pi ~\text{rad/s}^2\) 2. \(28\pi ~\text{rad/s}^2\)
3. \(120\pi ~\text{rad/s}^2\) 4. \(1 ~\text{rad/s}^2\)

Subtopic:  Rotational Motion: Kinematics |
 69%
From NCERT
NEET - 2020
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Three identical spheres, each of mass \(M\), are placed at the corners of a right-angle triangle with mutually perpendicular sides equal to \(2~\text{m}\) (see figure). Taking the point of intersection of the two mutually perpendicular sides as the origin, find the position vector of the centre of mass. 
        
1. \(2(\hat{i}+\hat{j})\)
2. \(\hat{i}+\hat{j}\)
3. \(\frac{2}{3}(\hat{i}+\hat{j})\)
4. \(\frac{4}{3}(\hat{i}+\hat{j})\)

Subtopic:  Center of Mass |
 64%
From NCERT
NEET - 2020
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A particle of mass \(5m\) at rest suddenly breaks on its own into three fragments. Two fragments of mass \(m\) each move along mutually perpendicular directions with speed \(v\) each. The energy released during the process is:
1. \(\frac{3}{5}mv^2\)
2. \(\frac{5}{3}mv^2\)
3. \(\frac{3}{3}mv^2\)
4. \(\frac{4}{3}mv^2\)

Subtopic:  Linear Momentum |
 58%
From NCERT
NEET - 2019
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A particle starting from rest moves in a circle of radius \(r\). It attains a velocity of \(v_0~\text{m/s}\) on completion of \(n\) rounds. Its angular acceleration will be:

1. \( \frac{v_0}{n} ~\text{rad} / \text{s}^2\) 2. \( \frac{v_0^2}{2 \pi {nr}^2}~ \text{rad} / \text{s}^2 \)
3. \( \frac{v_o^2}{4 \pi {n}{r}^2}~ \text{rad} / \text{s}^2 \) 4. \( \frac{v_0^2}{4 \pi {nr}} ~\text{rad} / \text{s}^2 \)

Subtopic:  Rotational Motion: Kinematics |
 51%
From NCERT
NEET - 2019
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An object flying in the air with velocity \((20 \hat{i}+25 \hat{j}-12 \hat{k})\) suddenly breaks into two pieces whose masses are in the ratio of \(1:5.\) The smaller mass flies off with a velocity \((100 \hat{i}+35 \hat{j}+8 \hat{k})\). The velocity of the larger piece will be:
1. \( 4 \hat{i}+23 \hat{j}-16 \hat{k}\)
2. \( -100 \hat{i}-35 \hat{j}-8 \hat{k} \)
3. \( 20 \hat{i}+15 \hat{j}-80 \hat{k} \)
4. \( -20 \hat{i}-15 \hat{j}-80 \hat{k}\)

Subtopic:  Linear Momentum |
 74%
From NCERT
NEET - 2019
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The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through:

         

1. \(C\)  2. \(D\)
3. \(A\) 4. \(B\)  
Subtopic:  Moment of Inertia |
 80%
From NCERT
AIPMT - 2012
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A circular platform is mounted on a frictionless vertical axle. Its radius \(R = 2~\text{m}\) and its moment of inertia about the axle is \(200~\text{kg m}^2\). It is initially at rest. A \(50~\text{kg}\) man stands on the edge of the platform and begins to walk along the edge at the speed of \(1~\text{ms}^{-1}\) relative to the ground. The time taken by man to complete one revolution is:
1. \(\frac{3\pi}{2}\text{s}\)
2. \(2\pi~\text{s}\)
3. \(\frac{\pi}{2}\text{s}\)
4. \(\pi~\text{s}\)

Subtopic:  Angular Momentum |
 64%
From NCERT
AIPMT - 2012
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Three masses are placed on the \(x\)-axis: \(300~\text{g}\) at origin, \(500~\text{g}\) at \(x= 40~\text{cm}\) and \(400~\text{g}\) at \(x= 70~\text{cm}\). The distance of the centre of mass from the origin is:
1. \(45~\text{cm}\)
2. \(50~\text{cm}\)
3. \(30~\text{cm}\)
4. \(40~\text{cm}\)

Subtopic:  Center of Mass |
 81%
From NCERT
AIPMT - 2012
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