System Of Particles And Rotational Motion Ques 91
91. 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) $5: 7$
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Answer:
Correct Answer: 91.(d)
Solution:
- (d) $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} $
$\therefore \frac{E_t}{E} =\frac{\frac{1}{2} m v^{2}}{\frac{7}{10} m v^{2}}=\frac{5}{7}$
BETA
