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%
From NCERT
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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%
From NCERT
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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%
From NCERT
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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%
From NCERT
PMT - 2004
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Two masses m1 and m2, m1 > m2 are connected to the ends of massless rope and allowed to move as shown in the figure. The acceleration of the centre of mass assuming pulley is massless and frictionless, is

1.  \(\frac{m_{1}   -   m_{2}}{m_{1}   +   m_{2}} g\)

2.  0

3.  \({m_1 -m_2^2 \over m_1 + m_2 } g \)

4.  \({m_1 +m_2^2 \over m_1 - m_2 } g \)

Subtopic:  Center of Mass |
 63%
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The speed of a uniform spherical shell after rolling down an inclined plane of vertical height h from rest is:

1.  \(\sqrt{\frac{10   g h}{7}}\)

2.    \(\sqrt{\frac{6   g h}{5}}\)

3.  \(\sqrt{\frac{4   g h}{5}}\)

4.  \(\sqrt{2   g h}\)

Subtopic:  Rolling Motion (OLD NCERT) |
 67%
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A uniform rod of mass m is bent into the form of a semicircle of radius R. The moment of inertia of the rod about an axis passing thorugh A and Perpendicular to the plane of paper is

1. 23MR2

2. MR2

3. 2MR2

4. 32MR2

Subtopic:  Moment of Inertia |
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A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity ω. Four objects each of mass m, are kept gently to the opposite ends of two perpendicular diameters of the ring. The angular velocity of the ring will be

1. MωM+4m

2.(M+4m)ωM

3. (M-4m)ωM+4m

4. Mω4m

Subtopic:  Angular Momentum |
 79%
From NCERT
PMT - 2003
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