A wheel comprises of a ring of radius R and mass M and three spokes of mass m each. The moment of inertia of the wheel about its axis is

                   

1.  \(\left(M   +   \frac{m}{4}\right) R^{2} \)

2.  \(\left(M   +   m\right) R^{2} \)

3.  \(\left(M   +   3 m\right) R^{2} \)

4.  \(\left(\frac{M   +   m}{2}\right) R^{2}\)

Subtopic:  Moment of Inertia |
 56%
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The angular velocity of a body changes from 125 rev./sec to 1 rev./sec. without applying any torque. The ratio of its radius of gyration in two situations is :

1.  5: 1

2.  1: 5

3.  1: 25

4.  25: 1

Subtopic:  Angular Momentum |
 65%
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A solid cylinder and a solid sphere, both having the same mass and radius, are released from a rough inclined plane. Both roll without slipping. Then,

1.  the force of friction that acts on the two is the same

2.  the force of friction is greater in the case of a sphere than in a cylinder

3.  the force of friction is greater in the case of a cylinder than in a sphere

4.  the force of friction will depend on the nature of the surface of the body that is moving and that of the inclined surface and is independent of the shape and size of the moving body

Subtopic:  Rolling Motion (OLD NCERT) |
 56%
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A homogeneous disc of mass 2 kg and radius 15 cm is rotating about its axis (which is fixed) with an angular velocity of 4 rad/sec. The linear momentum Of the disc is 

1.  1.2 kg m/sec 

2.  1.0 kg m/sec 

3.  0.6 kg m/sec 

4.  None of these

Subtopic:  Rotational Motion: Kinematics |
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A rigid body rotates about a fixed axis with a variable angular velocity equal to \(\alpha -\beta t\), at the time \(t\), where \(\alpha , \beta\) are constants. The angle through which it rotates before it stops is:

1. \(\frac{\alpha^{2}}{2 \beta}\) 2. \(\frac{\alpha^{2} -\beta^{2}}{2 \alpha}\)
3. \(\frac{\alpha^{2} - \beta^{2}}{2 \beta}\) 4. \(\frac{\left(\alpha-\beta\right) \alpha}{2}\)
Subtopic:  Rotational Motion: Kinematics |
 64%
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For the uniform T shaped structure, with mass \(3~ \text M\), the moment of inertia about an axis normal to the plane and passing through O would be

            

1. \({ 2 \over 3} \text {MI}^2\)
2. \(\text {MI}^2\)
3. \({ MI^2 \over 3}\)
4. None of these 

Subtopic:  Moment of Inertia |
 54%
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The moment of inertia of a disc about its own axis is \(I\). Its moment of inertia about a tangential axis in its plane is:
1. \(\frac{5}{2}I\)
2. \(3I\)
3. \(\frac{3}{2}I\)
4. \(4I\)
Subtopic:  Moment of Inertia |
 57%
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A rigid body rotates with an angular momentum L. If its rotational kinetic energy is made 4 times, its angular momentum will become

1.  4L

2.  16L

3.  2 L

4.  2L

Subtopic:  Angular Momentum |
 75%
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Four particles of mass \(m_1 = 2m\), \(m_2=4m\), \(m_3 =m \), and \(m_4\) are placed at the four corners of a square. What should be the value of \(m_4\) so that the centre of mass of all the four particles is exactly at the centre of the square?

Four particles of mass m1 = 2m, m2 = 4m, m3 = m and m4 are placed at four  corners of a square. What should be the value of m4 so that

1. \(2m\) 2. \(8m\)
3. \(6m\) 4. None of these
Subtopic:  Center of Mass |
 58%
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Angular momentum of a body is defined as the product of

1.  Mass and angular velocity

2.  Centripetal force and radius

3.  Linear velocity and angular velocity

4.  Moment of inertia and angular velocity

Subtopic:  Angular Momentum |
 87%
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PMT - 2004
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