Rotational Motion

JEE Main level, numerical answer, medium

259 of 280

Question 259 of 280

The following bodies,
(1)\left(1\right) a ring
(2)\left(2\right) a disc
(3)\left(3\right) a solid cylinder
(4)\left(4\right) a solid sphere,
of same mass mm and radius RR are allowed to roll down without slipping simultaneously from the top of the inclined plane. The body which will reach first at the bottom of the inclined plane is
[Mark the body as per their respective numbering given in the question]

Show answer and solution

Answer: 4

MgsinθR=(mk2+mR2)αMgsin\theta R=\left(m{k}^{2}+m{R}^{2}\right)\alpha
α=Rgsin⁡θk2+R2⇒a=gsin⁡θ1+k2R2\alpha =\dfrac{Rg\sin \theta }{{k}^{2}+{R}^{2}}\Rightarrow a=\dfrac{g\sin \theta }{1+\dfrac{{k}^{2}}{{R}^{2}}}
t=2sa=2sgsin⁡θ(1+k2R2)t=\sqrt{\dfrac{2s}{a}}=\sqrt{\dfrac{2s}{g\sin \theta }\left(1+\dfrac{{k}^{2}}{{R}^{2}}\right)}
for least time, kk should be least and we know kk, is least for the solid sphere.

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.