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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A disc of radius \(2~\text{m}\) and mass \(100~\text{kg}\) rolls on a horizontal floor. Its centre of mass has a speed of \(20~\text{cm/s}\). How much work is needed to stop it?
1. \(1~\text{J}\)
2. \(3~\text{J}\)
3. \(30~\text{J}\)
4. \(2~\text{J}\)

Subtopic:  Rotational Motion: Dynamics |
From NCERT
NEET - 2019
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A solid cylinder of mass \(2\) kg and radius \(4\) cm is rotating about its axis at the rate of \(3\) rpm. The torque required to stop after \(2\pi\) revolutions is:
1. \(2\times 10^6\) N-m
2. \(2\times 10^{-6}\) N-m
3. \(2\times 10^{-3}\) N-m
4. \(12\times 10^{-4}\) N-m

Subtopic:  Torque |
 64%
From NCERT
NEET - 2019
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A uniform rod of length \(l\) and mass \(M\) is free to rotate in a vertical plane about \(A\). The rod, initially in the horizontal position, is released. The initial angular acceleration of the rod is: (Moment of inertia of the rod about \(A\) is \(\frac{Ml^2}{3}\))
1. \(\frac{3g}{2l}\)
2. \(\frac{2l}{3g}\)
3. \(\frac{3g}{2l^2}\)
4. \(\frac{Mg}{2}\)

Subtopic:  Torque |
 74%
From NCERT
AIPMT - 2006
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The moment of inertia of a uniform circular disc of radius \(R\) and mass \(M\) about an axis touching the disc at its diameter and normal to the disc is:
1. MR2

2. 25MR2

3. 32MR2

4. 12MR2

Subtopic:  Moment of Inertia |
 68%
From NCERT
AIPMT - 2006
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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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A uniform rod AB of length \(l\) and mass \(m\) is free to rotate about point A. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about A is \(\frac{ml^2}{3}\) the initial angular acceleration of the rod will be: 
       
1. \(\frac{2g}{3l}\)
2. \(\frac{mgl}{2}\)
3. \(\frac{3}{2}gl\)
4. \(\frac{3g}{2l}\)

Subtopic:  Rotational Motion: Dynamics |
 76%
From NCERT
AIPMT - 2007
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A wheel has an angular acceleration of \(3.0\) rad/s2 and an initial angular speed of \(2.0\) rad/s. In a time of \(2\) s, it has rotated through an angle (in radians) of:

1. \(6\) 2. \(10\)
3. \(12\) 4. \(4\)

Subtopic:  Rotational Motion: Kinematics |
 83%
From NCERT
AIPMT - 2007
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