Question

A uniform disc of mass $M$ and radius $R$ rolls down an inclined (angle of inclination=$\theta$) plane without slipping then acceleration of COM is given by
$\frac{kgsin\theta }{3}$,then the value of $k$,is

Answer 1

$a=\frac{mg\sin \theta }{m}=f\alpha =\frac{2fr}{m{r}^2}=\frac{2f}{mr}r\alpha =a\Rightarrow \frac{2f}{m}\times r=g\sin \theta -\frac{f}{m}\frac{f}{m}=\frac{1}{3}g\sin \theta \Rightarrow a=\frac{2}{3}g\sin \theta \Rightarrow a=\frac{k}{3}g\sin \theta \Rightarrow k=2$

Hence the correct answer is $2$