The moment of inertia of a thin rod about an axis passing through its mid point and perpendicular to the rod is \(2400 ~\text{g cm}^2.\) The length of the \(400~\text{g}\) rod is nearly:
1. \(17.5~\text{cm}\) 2. \(20.7~\text{cm}\)
3. \(72.0~\text{cm}\) 4. \(8.5~\text{cm}\)
Subtopic:  Moment of Inertia |
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Consider a thin circular ring (A), a circular disc (B), a hollow Cylinder (C) and a solid cylinder (D) of the same radius R and of same mass: 
(A) (B)
(C) (D)
If \(I_A, I_B, I_C \) and \(I_D\) are their moments of inertia about the axis shown, then: 
Choose the correct answer from the options given below: 
1. \({I}_A={I}_C~ \text{and} ~2{I}_B={I}_D\)
2. \(I_A=2 I_B~ \text{and} ~2 I_C=I_D \)
3. \(2 I_A=I_C~ \text{and} ~I_B=2 I_D\)
4. \({I}_{{A}}={I}_B={I}_C=2 {I}_{{D}}\)
Subtopic:  Moment of Inertia |
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The radius of gyration of a solid sphere of mass \(5~\text{kg}\) about \(XY\) is \(5~\text m\) as shown in the figure. The radius of the sphere is \(\frac{5x}{\sqrt{7}}~\text m,\)then the value of \(x\) is:
                    
1. \(5\)
2. \(\sqrt{2}\)
3. \(\sqrt{3}\)
4. \(\sqrt{5}\)
 
Subtopic:  Moment of Inertia |
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The ratio of radius of gyration of a solid sphere of mass \(M\) and radius \(R\) about its own axis to the radius of gyration of the thin hollow sphere of same mass and radius about its axis is:
1. \(5:2\) 2. \(3:5\)
3. \(5:3\) 4. \(2:5\)
Subtopic:  Moment of Inertia |
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The ratio of the radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is: 
1. \(1:\sqrt{2}\) 2. \(2:1\)
3. \(\sqrt{2}:1\) 4. \(4:1\)
Subtopic:  Moment of Inertia |
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The ratio of the moments of inertia of two spheres, about their diameters, having the same mass and their radii being in the ratio of \(1:2\), is:

1. \(2:1\) 2. \(4:1\)
3. \(1:2\) 4. \(1:4\)
Subtopic:  Moment of Inertia |
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An energy of \(484\) J is spent in increasing the speed of a flywheel from \(60\) rpm to \(360\) rpm. The moment of inertia of the flywheel is:
1. \(0.7\) kg-m2 2. \(3.22\) kg-m2
3. \(30.8\) kg-m2 4. \(0.07\) kg-m2
Subtopic:  Moment of Inertia |
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From a circular ring of mass \({M}\) and radius \(R\), an arc corresponding to a \(90^\circ\) sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is \(K\) times \(MR^2\). The value of \(K\) will be:

1. \(\dfrac{1}{4}\) 2. \(\dfrac{1}{8}\)
3. \(\dfrac{3}{4}\) 4. \(\dfrac{7}{8}\)
Subtopic:  Moment of Inertia |
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A light rod of length \(l\) has two masses, \(m_1\) and \(m_2,\) attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is:
1. \(\frac{m_1m_2}{m_1+m_2}l^2\)
2. \(\frac{m_1+m_2}{m_1m_2}l^2\)
3. \((m_1+m_2)l^2\)
4. \(\sqrt{(m_1m_2)}l^2\)

Subtopic:  Moment of Inertia |
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From a disc of radius \(R\) and mass \(M\), a circular hole of diameter \(R\), whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis, passing through the centre?
1. \(\frac{13}{32}MR^2\)
2. \(\frac{11}{32}MR^2\)
3. \(\frac{9}{32}MR^2\)
4. \(\frac{15}{32}MR^2\)
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