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