Question

A thin uniform circular ring is rolling down an inclined plane of induction 30$^\circ$ without slipping, its linear acceleration along the inclined plane will be

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

Answer 1

Answer: (C)

$\frac {g}{4}$

Answer 2

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