A uniform solid cylinder of mass ' $m$ ' and radius ' $r$ ' rolls along an inclined rough plane of i

Question

A uniform solid cylinder of mass ' $m$ ' and radius ' $r$ ' rolls along an inclined rough plane of inclination $45^{\circ}$. If it starts to roll from rest from the top of the plane then the linear acceleration of the cylinder's axis will be\

Professor PC Thomas Classes · Answer

(c) : Given, mass of solid cylinder $=m$ Radius of solid cylinder $=r$\ Moment of inertia for a solid cylinder, $I=\frac{1}{2} m r^{2}$\ ∵ Acceleration, $a=\frac{g \sin 	heta}{1+\frac{I}{m r^{2}}} ; a=\frac{g \sin 45^{\circ}}{1+\frac{1}{2}}$\ $ a=\frac{g}{\sqrt{2}}\left(\frac{2}{3}ight) \Rightarrow a=\frac{\sqrt{2} g}{3} $