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  4. The moment of inertia of a solid cylinder about its axis is given by (1/2)MR2 . If this cylinder rolls without shipping the ratio of its rotational kinetic energy to its translational kinetic energy is-

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Q. The moment of inertia of a solid cylinder about its axis is given by $\frac{1}{2}MR^{2}$ . If this cylinder rolls without shipping the ratio of its rotational kinetic energy to its translational kinetic energy is-

NTA AbhyasNTA Abhyas 2020System of Particles and Rotational Motion

Solution:

$K_{R}=\frac{1}{2}I\omega ^{2} \, \, \, \Rightarrow \, \, \, K_{R}=\frac{1}{2}\times \frac{1}{2}mR^{2}\frac{v^{2}}{R^{2}}\Rightarrow K_{R}=\frac{1}{2}.\frac{1}{2}mv^{2}$
$K_{R}=\frac{1}{2}K_{T} \, \Rightarrow \, \frac{K_{R}}{K_{T}}=\frac{1}{2}$