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)

Acceleration of the solid sphere slipping down the incline without rolling is
$a_{\text{slipping }}=g\sin \theta \dots (i)$
Acceleration of the solid sphere rolling down the incline without slipping is
$a_{\text{rolling }}=\frac{g\sin \theta }{1+\frac{k^2}{R^2}}=\frac{g\sin \theta }{1+\frac{2}{5}}$
$(\therefore$ For solid sphere, $\frac{k^2}{R^2}=\frac{2}{5})$
$=\frac{5}{7}g\sin \theta ..(ii)$
Divide eqn. (ii) by eqn. (i), we get
$\frac{a_{\text{rolling }}}{a_{\text{slipping }}}=\frac{5}{7}$