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JEE Main 202524 JanuaryMorning Shift
Exam
JEE Main
Year
2025
Date
24 January
Shift
Morning Shift
Subject
Physics
Chapter
Rotational Motion

JEE Main 2025 · 24 January · Morning Shift · Physics · Rotational Motion

A uniform solid cylinder of mass ' m ' and radius ' r ' rolls along...

A uniform solid cylinder of mass ' mm ' and radius ' rr ' rolls along an inclined rough plane of inclination 45∘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

Options

  1. A12 g\frac{1}{\sqrt{2}} \mathrm{~g}
  2. B132 g\frac{1}{3 \sqrt{2}} \mathrm{~g}
  3. C2 g3\frac{\sqrt{2} \mathrm{~g}}{3}
  4. D2g\sqrt{2} g

Correct answer

C. 2 g3\frac{\sqrt{2} \mathrm{~g}}{3}

Step-by-step solution

a=gsin⁡θ1+ImR2a=g21+12=2g23=2g3\begin{aligned} & a=\frac{\mathrm{g} \sin \theta}{1+\frac{\mathrm{I}}{\mathrm{mR}^2}} \\ & a=\frac{\frac{g}{\sqrt{2}}}{1+\frac{1}{2}}=\frac{2 \frac{g}{\sqrt{2}}}{3}=\frac{\sqrt{2} g}{3}\end{aligned})$
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