System of Particles and Rotational Motion - Result Question 73
80. 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
[2018]
(a) $7: 10$
(b) $5: 7$
(c) $2: 5$
(d) $10: 7$
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Answer:
Correct Answer: 80. (b)
Solution:
- (b) In rolling motion, rotational kinetic energy.
$ K_t=\frac{1}{2} m v^{2} $
And, $K_t+K_r=\frac{1}{2} m v^{2}+\frac{1}{2} l \omega^{2}$
$=\frac{1}{2} m v^{2}+\frac{1}{2}(\frac{2}{5} m r^{2})(\frac{v}{r})^{2}=\frac{7}{10} m v^{2}$
$\therefore \quad \frac{K_t}{K_t+K_r}=\frac{\frac{1}{2} m v^{2}}{\frac{7}{10} m v^{2}}=\frac{5}{7}$
