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's axis will be (a) √(2) g (b) 1/√(2) g (c) (1)/(3√(2)) g (d) (√(2)g)/(3)

Answer: (d). Rolling down an incline: a = (gsin θ)/(1+k); solid cylinder k = 1/2. a = 2/3gsin 45° = 2/3/√(2) = (√(2) g)/(3). So the answer is (d).

A uniform solid cylinder of mass ' m ' and radius ' r ' rolls along… | JEE Main 2025 (24 Jan, Shift 1)

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Rolling Motion

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

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Answer: (d)

Rolling down an incline: $a = \dfrac{g\sin\theta}{1+k}$ ; solid cylinder $k = \frac{1}{2}$ .
$a = \dfrac{2}{3}g\sin 45^\circ = \dfrac{2}{3}\cdot\dfrac{g}{\sqrt{2}} = \dfrac{\sqrt{2}\,g}{3}$ .
So the answer is (d).

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