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  4. A cylinder is rolling down a inclined plane of inclination 60° . What is its acceleration?

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Q. A cylinder is rolling down a inclined plane of inclination $60^{\circ} $ . What is its acceleration?

Delhi UMET/DPMTDelhi UMET/DPMT 2008System of Particles and Rotational Motion

Solution:

For cylinder, $I=\frac{1}{2} MR^{2}=1\, MR\, 2$
So, $\frac{K^{2}}{R^{2}}=\frac{1}{2}$
So. acceleration $a=\frac{g \sin \theta}{1+\frac{K^{2}}{R^{2}}}$
$=\frac{g \sin 60^{\circ}}{1 +\frac{1}{2}}=\frac{g}{\sqrt{3}}$