Physics - Rotation Question with Solution | TestHub

PhysicsRotationTranslational + RotationalEasy2 minPYQ_2018

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A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy $(K_{t})$ as well as rotational kinetic energy $(K_{r})$ simultaneously. The ratio $K_{t} : (K_{t} + K_{r})$ for the sphere isNEET 2018

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Answer:

Solution:

Transnational $K E$ $= \frac{1}{2} m v^{2}$
Translational $K E +$ Rotational $K E$
$= \frac{1}{2} m v^{2} + \frac{1}{2} I ω^{2}$
$= \frac{1}{2} m v^{2} + \frac{1}{2} (\frac{2}{5} m r^{2}) ω^{2}$
$∵$ for rolling motion $v = r ω$
$= \frac{1}{2} m v^{2} + \frac{1}{2} \times \frac{2}{5} m r^{2} {(\frac{v}{r})}^{2} = \frac{7}{10} m v^{2}$
So, $\frac{K_{t}}{K_{t} + K_{r}} = \frac{\frac{1}{2} m v^{2}}{\frac{7}{10} m v^{2}} = \frac{5}{7}$

Stream:NEETSubject:PhysicsTopic:RotationSubtopic:Translational + Rotational

⏱ 2mℹ️ Source: PYQ_2018

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