Question

A solid cylinder of mass $M$ and radius $R$ rolls without slipping down an inclined plane making an angle 6 with the horizontal. Then its acceleration is

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

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, $k^{2}=\frac{R^{2}}{2}$
$\therefore \quad a=\frac{g \sin \theta}{1+\frac{1}{2}}=\frac{2}{5} g \sin \theta$