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JEE MAIN 2025
24-01-2025 SHIFT-1
Question
A uniform solid cylinder of mass 'm' and radius 'r' rolls along an inclined rough plane of inclination $45º$. If it starts to roll from rest from the top of the plane then the linear acceleration of the cylinder's axis will be
Select the correct option:
A
$\frac{1}{{\sqrt 2 }}g$
B
$\sqrt 2 g$
C
$\frac{{\sqrt 2 \;{\rm{g}}}}{3}$
D
$\frac{1}{{3\sqrt 2 }}\;{\rm{g}}$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
$a = \frac{{g\sin \theta }}{{1 + \frac{I}{{{m^2}}}}}$
$a = \frac{{\frac{{\rm{g}}}{{\sqrt 2 }}}}{{1 + \frac{1}{2}}} = \frac{{2\frac{{\;{\rm{g}}}}{{\sqrt 2 }}}}{3} = \frac{{\sqrt 2 g}}{3}$
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