Three-point masses 'm' each, are placed at the vertices of an equilateral triangle of side a. Moment of inertia of the system about axis COD is-

          

1. 2ma2

2. 23ma2

3. 54ma2

4. 74ma2

Subtopic:  Moment of Inertia |
 66%
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A particle is moving in a circular orbit with constant speed. Select wrong alternate

1. Its linear momentum is conserved
2. Its angular momentum is conserved
3. It is moving with variable velocity
4. It is moving with variable acceleration
Subtopic:  Linear Momentum |
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An \(ABC\) is a right-angled triangular plate of uniform thickness. The sides are such that \(AB>BC\). As shown in the figure \(I_1,I_2\) and \(I_3\) are moments of inertia about \(AB, BC\) and \(AC\) respectively. Which of the following relation is correct?

             

1. \(I_1 = I_2 = I_3\) 2. \(I_2 > I_1 > I_3\)
3. \(I_3 > I_2 > I_1\) 4. \(I_3 > I_1 > I_2\)
Subtopic:  Moment of Inertia |
 51%
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One solid sphere A and another hollow sphere B are of same mass and same outer radii. Their moment of inertia about their diameters are respectively \(\text{I}_{A}\) and \(\text{I}_{B}\) such that
1. \(\text{I}_{\text{A}}=\text{I}_{\text{B}}\)
2. \(\text{I}_{\text{A}}>\text{I}_{\text{B}}\)
3. \(\text{I}_{\text{A}}<\text{I}_{\text{B}}\)
4. \(\frac{\text{I}_{\text{A}}}{\text{I}_{\text{B}}}=\frac{d_A}{d_B}\)

Subtopic:  Moment of Inertia |
 74%
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A particle of mass \(1 ~\text{kg}\) is kept at (1m, 1m, 1m). \((1~\text{m},~1~\text{m},~1~\text{m}),\) The moment of inertia of this particle about \(z-\)axis would be
1. \(1~\text{kg}-\text{m}^2\)
2. \(2~\text{kg}-\text{m}^2\)
3. \(3~\text{kg}-\text{m}^2\)
4. None of these

Subtopic:  Moment of Inertia |
 51%
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A horizontal platform is rotating with uniform angular velocity around the vertical axis passing through its centre. At some instant of time a viscous fluid of mass 'm' is dropped at the centre and is allowed to spread out and finally fall. The angular velocity during this period

1. Decreases continuously

2. Decreases initially and increases again

3. Remains unaltered

4. Increases continuously

Subtopic:  Angular Momentum |
 58%
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AIIMS - 2005
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For \(L = 3.0~\text{m,}\) the total torque about pivot A provided by the forces as shown in the figure is:

1. \(210 ~\text{Nm}\) 2. \(140 ~\text{Nm}\)
3. \(95 ~\text{Nm}\) 4. \(75 ~\text{Nm}\)
Subtopic:  Torque |
 59%
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For the same total mass, which of the following will have the largest moment of inertia about an axis passing through the centre of gravity and perpendicular to the plane of the body?
1. A disc of radius \(a\)
2. a ring of radius \(a\)
3. a square lamina of side \(2a\)
4. four rods forming square of side \(2a\)

Subtopic:  Moment of Inertia |
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The radius of gyration of a uniform rod of length \(L\) about an axis passing through its centre of mass is
1. \(\frac{L}{2 \sqrt{3}}\)
2. \(\frac{L^2}{12}\)
3. \(\frac{L}{\sqrt{3}}\)
4. \(\frac{L}{\sqrt{2}}\)

Subtopic:  Moment of Inertia |
 73%
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Two uniform, thin, identical rods, each of mass \(M\) and length \(l\) are joined together to form a cross. What will be the moment of inertia of the cross about an axis passing through the point at which the two rods are joined and are perpendicular to the plane of the cross?
1. \(\frac{Ml^2}{12}\)
2. \(\frac{Ml^2}{6}\)
3. \(\frac{Ml^2}{4}\)
4. \(\frac{Ml^2}{3}\)

Subtopic:  Moment of Inertia |
 77%
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