System of Particles and Rotational Motion - Result Question 85
92. If a sphere is rolling, the ratio of the translational energy to total kinetic energy is given by [1991]
(a) $7: 10$
(b) $2: 5$
(c) $10: 7$
(d) $5: 7$
Show Answer
Answer:
Correct Answer: 92. (d)
Solution:
$ \begin{aligned} E & =E_t+E_r=\frac{1}{2} m v^{2}+\frac{1}{2} I \omega^{2} \\ & =\frac{1}{2} m v^{2}+\frac{1}{2} \times(\frac{2}{5} m r^{2}) \omega^{2} \\ & =\frac{1}{2} m v^{2}+\frac{1}{5} m v^{2}=\frac{7}{10} m v^{2} \\ \therefore \frac{E_t}{E} & =\frac{\frac{1}{2} m v^{2}}{\frac{7}{10} m v^{2}}=\frac{5}{7} \end{aligned} $
