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 ’ θ ’ 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:

  1. (a) For solid sphere rolling without slipping on inclined plane, acceleration

a1=gsinθ(1+K2R2)

For solid sphere slipping on inclined plane without rolling, acceleration

a2=gsinθ

Therefore required ratio =a1a2

=1(1+K2R2)=1(1+25)=57



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