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

Answer: (A)

5 : 7

Answer 2

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
$\frac{a_{rolling}}{a_{slipping}} = \frac{5}{7}$