System of Particles and Rotational Motion - Result Question 76

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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 :

======= ####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 :

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/system-of-particles-and-rotational-motion/system-of-particles-and-rotational-motion—result-question-76.md (a) $5: 7$

(b) $2: 3$

(c) $2: 5$

(d) $7: 5$

[2014]

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Answer:

Correct Answer: 83. (a)

Solution:

  1. (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 $=\frac{a_1}{a_2}$

$=\frac{1}{(1+\frac{K^{2}}{R^{2}})}=\frac{1}{(1+\frac{2}{5})}=\frac{5}{7}$