Question

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

Answer 1

The Correct Option is A

The correct answer is A:\(5\ratio 7\)
Acceleration of the solid sphere slipping down the incline without rolling is 
\(a_{slipping} = gsin \theta...(i)\) 
Acceleration of the solid sphere rolling down the incline without slipping is 
\(a_{rolling} = \frac{gsin\theta}{1 + \frac{k^2}{R^2}} = \frac{gsin\theta}{1 + \frac{2}{5}}\)
\(\bigg(\)\(\therefore\) For solid sphere, \(\frac{k^2}{R^2} = \frac{2}{5}\)\(\bigg)\)
\(= \frac{5}{7} gsin\theta ...(ii)\) 
Divide eqn. (ii) by eqn. (i), we get 
\(\frac{a_{rolling}}{a_{slipping}} = \frac{5}{7}\)