Question

A thin uniform circular ring is rolling down an inclined plane of inclination 30° without slipping. Its linear acceleration along the inclined plane will be

• A. $\frac{g}{2}$
• B. $\frac{g}{3}$
• C. $\frac{g}{4}$
• D. $\frac{2g}{3}$

Answer 1

Answer: (C)

$\frac{g}{4}$

Answer 2

$a = \frac{g\sin\theta}{1 + \frac{k^{2}}{R^{2}}} = \frac{g\sin 30^{o}}{1 + 1} = \frac{g}{4}$

[As $\frac{k^{2}}{R^{2}} = 1$ and $\theta = 30^{o}$]