System Of Particles And Rotational Motion Ques 78

78. 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) $10: 7$

Show Answer

Answer:

Correct Answer: 78.(b)

Solution:

  1. (b) In rolling motion, rotational kinetic energy.

$ K_t=\frac{1}{2} m v^{2} $

And, $K_t+K_r=\frac{1}{2} m v^{2}+\frac{1}{2} l \omega^{2}$

$=\frac{1}{2} m v^{2}+\frac{1}{2}(\frac{2}{5} m r^{2})(\frac{v}{r})^{2}=\frac{7}{10} m v^{2}$

$\therefore \quad \frac{K_t}{K_t+K_r}=\frac{\frac{1}{2} m v^{2}}{\frac{7}{10} m v^{2}}=\frac{5}{7}$

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