System of Particles and Rotational Motion - Result Question 76
83. The ratio of the accelerations for a solid sphere (mass ’ $m$ ’ and radius ’ $R$ ‘) rolling down an incline of angle ’ $\theta$ ’ without slipping and slipping down the incline without rolling is :
(a) $5: 7$
(b) $2: 3$
(c) $2: 5$
(d) $7: 5$
[2014]
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Answer:
Correct Answer: 83. (a)
Solution:
- (a) For solid sphere rolling without slipping on inclined plane, acceleration
$ a_1=\frac{g \sin \theta}{(1+\frac{K^{2}}{R^{2}})} $
For solid sphere slipping on inclined plane without rolling, acceleration
$ a_2=g \sin \theta $
Therefore required ratio $=\frac{a_1}{a_2}$
$=\frac{1}{(1+\frac{K^{2}}{R^{2}})}=\frac{1}{(1+\frac{2}{5})}=\frac{5}{7}$
