Q. No.The moment of inertia of the object depends upon:
1. distribution of mass
2. axis of rotation of the body
3. shape and size of the body
4. all of the above
Subtopic: Â Moment of Inertia |
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A cricket mat of mass \(50\text{ kg}\) is rolled loosely in the form of a cylinder of radiys \(2\text{ m}.\) Now, again it is rolled tightly so that the radius becomes \(\left(\dfrac{3}{4} \right)^{\text{th}} \) of original value; then the ratio of moment of inertia of mat in the two cases is:
1. \(1:3\)
2. \(4:3\)
3. \(16:9\)
4. \(3:5\)
1. \(1:3\)
2. \(4:3\)
3. \(16:9\)
4. \(3:5\)
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For a uniform disc, the moment of inertia about diameter is \(\dfrac{MR^{2}}{4},\) where \(M\) is mass and \(R\) is radius of the disc. The moment of inertia about tangent parallel to diameter is:
| 1. | \(\dfrac{3}{4}MR^{2}\) | 2. | \(\dfrac{5}{4}MR^{2}\) |
| 3. | \(\dfrac{3}{2}MR^{2}\) | 4. | \(\dfrac{5}{2}MR^{2}\) |
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Consider two wheels, \(P\) and \(Q,\) connected via a belt drive system, \(B.\) If the radius of \(P\) is three times the radius of \(Q,\) and the rotational kinetic energies of both wheels are identical, what is the value of \(x\) in the expression \(\dfrac{I_1}{I_2}=\dfrac{x}{1},\) where \(I_1\) and \(I_2\) represent the moments of inertia of wheels \(P\) and \(Q,\) respectively?
1. \(2\)
2. \(4\)
3. \(9\)
4. \(11\)
1. \(2\)
2. \(4\)
3. \(9\)
4. \(11\)
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A thin circular disk is in the \(xy\) plane as shown in the figure. The ratio of its moment of inertia about \(z\) and \(z'\) axes will be:
1. \(1 : 4\)
2. \(1 : 5\)
3. \(1 : 3\)
4. \(1 : 2\)
1. \(1 : 4\)
2. \(1 : 5\)
3. \(1 : 3\)
4. \(1 : 2\)
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A solid sphere and a ring have equal masses and equal radii of gyration. If the sphere is rotating about its diameter and the ring about an axis passing through and perpendicular to its plane, then the ratio of the radii is \(\sqrt{\dfrac{x}{2}}.\) The value of \(x\) is:
1. \(5\)
2. \(2\)
3. \(1\)
4. \(4\)
1. \(5\)
2. \(2\)
3. \(1\)
4. \(4\)
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Moments of inertia of two rings are in the ratio of \(2 : 1\) and their diameters are in the ratio of \(4:1\). The ratio of their respective masses will be:
1. \(1 : 4\)
2. \(4 : 1\)
3. \(6 : 1\)
4. \(1 : 8\)
1. \(1 : 4\)
2. \(4 : 1\)
3. \(6 : 1\)
4. \(1 : 8\)
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The radius of gyration of a cylindrical rod of length \(10 \sqrt 3\) m about an axis of rotation perpendicular to its length and passing through the center will be:
1. \(5\) m
2. \(3\) m
3. \(1\) m
4. \(4\) m
1. \(5\) m
2. \(3\) m
3. \(1\) m
4. \(4\) m
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The moment of inertia of a disc about one of its diameters is:
| 1. | \(MR^2\) | 2. | \(\dfrac{MR^2}{3}\) |
| 3. | \(\dfrac{2MR^2}{3}\) | 4. | \(\dfrac{MR^2}{4}\) |
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The moment of inertia of a uniform circular disc of radius \(R\) and mass \(M\) about an axis passing through the centre and perpendicular to its plane is:
1. \(\dfrac14MR^2\)
2. \(\dfrac12MR^2\)
3. \(MR^2\)
4. \(\dfrac32MR^2\)
1. \(\dfrac14MR^2\)
2. \(\dfrac12MR^2\)
3. \(MR^2\)
4. \(\dfrac32MR^2\)
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