A solid sphere of mass m and radius R is rotating about its diameter. A soild cyclinder of the same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation Esphere/Ecylinder  will be 

(a) 2:3

(b) 1:5

(c) 1:4

(d) 3:1

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. \(\frac{15}{32}MR^2\)
Subtopic:  Moment of Inertia |
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