Rotational Motion

JEE Main level, numerical answer, medium

256 of 280

Question 256 of 280

Two bodies, a ring and a solid cylinder of same material are rolling down without slipping an inclined plane. The radii of the bodies are same. The ratio of velocity of the centre of mass at the bottom of the inclined plane of the ring to that of the cylinder is x2.\dfrac{\sqrt{x}}{2}. Then, the value of xx is

Show answer and solution

Answer: 3

In both, cases is about point of contact ring,
mgh=12Iω2mgh=\dfrac{1}{2}I{\omega }^{2}
mgh=12(2mR2)VR2R2mgh=\dfrac{1}{2}\left(2m{R}^{2}\right)\dfrac{{V}_{R}^{2}}{{R}^{2}}
VR=gh{V}_{R}=\sqrt{gh}
Solid cylinder
mgh=12Iω2mgh=\dfrac{1}{2}I{\omega }^{2}
mgh=12(32mR2)vC2R2mgh=\dfrac{1}{2}\left(\dfrac{3}{2}m{R}^{2}\right)\dfrac{{v}_{C}^{2}}{{R}^{2}}
vC=4gh3{v}_{C}=\sqrt{\dfrac{4gh}{3}}
vRvC=32\dfrac{{v}_{R}}{{v}_{C}}=\dfrac{\sqrt{3}}{2}

JEE Main question paper PDF

Open a shift to read the full paper on this page, or download it.

JEE Main 2025 Apr 2 Shift 1 question paper

Open Download PDF

Opening paper…

Explain it as a whiteboard videoStep-by-step, in Hinglish or English. Your first video needs no login.Solved it on paper but got it wrong?Upload a photo of your working. Mistake Doctor marks the exact line that broke.
See it move: Rotational dynamics and rolling simulationDrag the sliders and watch the numbers in this question change.Revise Rotational Motion firstFormula sheet, solved examples and the traps students fall into.

More Physics practice

JEE Main Physics practice question on Rotational Motion (Rolling without Slipping), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.