Question

A rolling object rolls without slipping down an inclined plane (angle of inclination $\theta$ ). If the minimum acceleration it can have is $\frac{g \sin \theta}{n}$. The value of $n$ is ___.

Answer 1

$a=\frac{g \sin \theta}{1+\frac{I}{M R^{2}}}$
$a$ is minimum, if $I$ is maximum.
$I_{\max } =M R^{2} $ [for ring]
$\Rightarrow a_{\min } =\frac{g \sin \theta}{1+\frac{M R^{2}}{M R^{2}}}=\frac{g \sin \theta}{2}$