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  4. A solid sphere of mass m and radius R is rotating about its diameter. A solid cylinder 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 (E textsphere / E textcylinder) Will be

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Q. A solid sphere of mass $m$ and radius $R$ is rotating about its diameter. A solid cylinder 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 $(E_{\text{sphere}} / E_{\text{cylinder}})$ Will be

NEETNEET 2016System of Particles and Rotational Motion

Solution:

$K \cdot E =\frac{1}{2} I \omega^{2}$
$\frac{ K \cdot E _{\text {sphere }}}{ K \cdot E _{\text {cylinder }}}=\frac{ I _{\text {sphere }}}{ I _{\text {cylinder }}} \quad\left(\frac{\omega_{\text {sphere }}}{\omega_{\text {cylinder }}}\right)^{2}$
$=\frac{\frac{2}{5} MR ^{2}}{\frac{ MR ^{2}}{2}}\left(\frac{\omega}{2 \omega}\right)^{2}$
$=\frac{4}{5} \times \frac{1}{4}=1: 5$