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_ - Physics MCQ NEET (UG) 2018 2026 | ExamTest.live

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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 is:

Solution & Step-by-step Explanation

1. Translational KE K_{t} = \frac{1}{2} M v^{2} .2. Rotational KE K_{r} = \frac{1}{2} I ω^{2} = \frac{1}{2} (\frac{2}{5} M R^{2}) (\frac{v}{R})^{2} = \frac{1}{5} M v^{2} .3. Total KE K = K_{t} + K_{r} = \frac{1}{2} M v^{2} + \frac{1}{5} M v^{2} = \frac{7}{10} M v^{2} .4. Ratio: \frac{K _{t}}{K _{t} + K _{r}} = \frac{\frac{1}{2} M v ^{2}}{\frac{7}{10} M v ^{2}} = \frac{1}{2} \times \frac{10}{7} = \frac{5}{7}

Try it yourself before checking the explanation above.

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 is:

10 : 7

5 : 7

7 : 10

2 : 5

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