A uniform solid cylinder of mass 'm' and radius 'r' rolls along an inclined rough plane of inclination 45°. If it starts to roll from rest from the top of the plane then the linear acceleration of the cylinder axis will be: [2025]

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Solution

Q.
A uniform solid cylinder of mass 'm' and radius 'r' rolls along an inclined rough plane of inclination 45°. If it starts to roll from rest from the top of the plane then the linear acceleration of the cylinder axis will be: [2025]

1 $\frac{1}{\sqrt{2}} g$

2 $\frac{1}{3 \sqrt{2}} g$

3 $\frac{\sqrt{2} g}{3}$

4 $\sqrt{2} g$

Ans.
(3)

$a = \frac{g \sin θ}{1 + \frac{I}{m r^{2}}}$

$a = \frac{\frac{g}{\sqrt{2}}}{1 + \frac{1}{2}} = \frac{2 \frac{g}{\sqrt{2}}}{3} = \frac{\sqrt{2} g}{3}$

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