Three objects, A: (a solid sphere), B: (a thin circular disk) and C: (a circular ring), each have the same mass \(\mathrm{M}\) and radius \(\mathrm{R}.\) They all spin with the same angular speed about their own symmetry axes. The amount of work (\(\mathrm{W}\)) required to bring them to rest, would satisfy the relation:

1. \(\mathrm{W_C}>\mathrm{W_B}>\mathrm{W_A} ~~~~~~~~\)
2. \(\mathrm{W_A}>\mathrm{W_B}>\mathrm{W_C}\)
3. \(\mathrm{W_B}>\mathrm{W_A}>\mathrm{W_C}\)
4. \(\mathrm{W_A}>\mathrm{W_C}>\mathrm{W_B}\)

Subtopic:  Rotational Motion: Kinematics |
 70%
From NCERT
NEET - 2018
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Which of the following statements are correct? 

a. centre of mass of a body always coincides with the centre of gravity of the body .
b. centre of gravity of a body is the point about which the total gravitational torque on the body is zero.
c. a couple on a body produce both translational and rotation motion in a body.
d. mechanical advantage greater than one means that small effort can be used to lift a large load.
 
1. (a) and (b) 2. (b) and (c)
3. (c) and (d) 4. (b) and (d)
Subtopic:  Center of Mass |
 59%
From NCERT
NEET - 2017
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The moment of the force, \(\overset{\rightarrow}{F} = 4 \hat{i} + 5 \hat{j} - 6 \hat{k}\) at point (\(2,\) \(0,\) \(-3\)) about the point (\(2,\) \(-2,\) \(-2\)) is given by:
1. \(- 8 \hat{i} - 4 \hat{j} - 7 \hat{k}\)
2. \(- 4 \hat{i} - \hat{j} - 8 \hat{k}\)
3. \(- 7 \hat{i} - 8 \hat{j} - 4 \hat{k}\)
4. \(- 7 \hat{i} - 4 \hat{j} - 8 \hat{k}\)

Subtopic:  Torque |
 70%
From NCERT
NEET - 2018
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A solid sphere is in rolling motion. In rolling motion, a body possesses translational kinetic energy (Kt) as well as rotational kinetic energy (Kr) simultaneously. The ratio K: (Kt + Kr) for the sphere will be:

1. 7:10

2. 5:7

3. 10:7

4. 2:5

Subtopic:  Rolling Motion (OLD NCERT) |
 80%
From NCERT
NEET - 2018
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A uniform circular disc of radius \(50\) cm at rest is free to turn about an axis that is perpendicular to its plane and passes through its centre. It is subjected to a torque that produces a constant angular acceleration of \(2.0\) rad s-2. Its net acceleration in ms-2 at the end of \(2.0\) s is approximately:
1. \(7\)
2. \(6\)
3. \(3\)
4. \(8\)

Subtopic:  Rotational Motion: Dynamics |
 57%
From NCERT
NEET - 2016
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A mass \(m\) moves in a circle on a smooth horizontal plane with velocity \(v_0\) at a radius \(R_0\). The mass is attached to a string that passes through a smooth hole in the plane, as shown.
   
The tension in the string is increased gradually and finally, \(m\) moves in a circle of radius \(\frac{R_0}{2}\). The final value of the kinetic energy is:
1. \( m v_0^2 \)
2. \( \frac{1}{4} m v_0^2 \)
3. \( 2 m v_0^2 \)
4. \( \frac{1}{2} m v_0^2\)

Subtopic:  Angular Momentum |
 58%
From NCERT
NEET - 2015
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Three identical spherical shells, each of mass \(m\) and radius \(r\) are placed as shown in the figure. Consider an axis \(XX'\), which is touching two shells and passing through the diameter of the third shell. The moment of inertia of the system consisting of these three spherical shells about the \(XX'\) axis is:
           

1. \(\frac{11}{5}mr^2\) 2. \(3mr^2\)
3. \(\frac{16}{5}mr^2\) 4. \(4mr^2\)

Subtopic:  Moment of Inertia |
 60%
From NCERT
NEET - 2015
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A solid cylinder of mass \(3\) kg is rolling on a horizontal surface with a velocity of \(4\) ms-1. It collides with a horizontal spring of force constant \(200\) Nm-1. The maximum compression produced in the spring will be:
1. \(0.5\) m
2. \(0.6\) m
3. \(0.7\) m
4. \(0.2\) m

Subtopic:  Rolling Motion (OLD NCERT) |
 63%
From NCERT
AIPMT - 2012
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Two particles that are initially at rest, move towards each other under the action of their mutual attraction. If their speeds are \(v\) and \(2v\) at any instant, then the speed of the centre of mass of the system will be:
1. \(2v\)
2. \(0\)
3. \(1.5v\)
4. \(v\)

Subtopic:  Center of Mass |
 78%
From NCERT
AIPMT - 2010
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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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