Question

A solid cylinder of mass $M$ and radius $R$ rolls down an inclined plane which has an angle of inclination $\theta $ . Find the acceleration of this rolling cylinder if it rolls without slipping.

• A. $\frac{1}{23}gsin \theta $
• B. $\frac{2}{3}gsin \theta $
• C. $\frac{2}{5}gsin \theta $
• D. $\frac{2}{7}gsin \theta $

Answer 1

Answer: (B)

Acceleration of a rolling body down an inclined plane is $a=\frac{g sin \theta }{1 + \frac{K^{2}}{R^{2}}}$
For solid cylinder, $K^{2}=\frac{R^{2}}{2}$
$\therefore a=\frac{g sin \theta }{1 + \frac{1}{2}}=\frac{2}{3}gsin ⁡ \theta $