Rotational Motion

JEE Main level, single correct, medium

71 of 280

Question 71 of 280



Three solid spheres each of mass mm and diameter dd are stuck together such that the lines connecting the centres form an equilateral triangle of side of length dd . The ratio I0IA\dfrac{{I}_{0}}{{I}_{A}} of moment of inertia I0{I}_{0} of the system about an axis passing the centroid and about center of any of the spheres IA{I}_{A} and perpendicular to the plane of the triangle is:

Show answer and solution

Answer: (A) 1323\dfrac{13}{23}

M.I about O =3[25M(d2)2+M(d3)2]=1310Md2=3\left[\dfrac{2}{5}M{\left(\dfrac{d}{2}\right)}^{2}+M{\left(\dfrac{d}{\sqrt{3}}\right)}^{2}\right]=\dfrac{13}{10}M{d}^{2}
M.I about A =2[25M(d2)2+M(d)2]+25M(d2)2=2310Md2=2\left[\dfrac{2}{5}M{\left(\dfrac{d}{2}\right)}^{2}+M{\left(d\right)}^{2}\right]+\dfrac{2}{5}M{\left(\dfrac{d}{2}\right)}^{2}=\dfrac{23}{10}M{d}^{2}
Now ratio =1323=\dfrac{13}{23}

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 (Moment of inertia of rigid bodies), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.