JEE Mains · Physics · STD 11 - System of particles and rotational motion
- JEE Mains 2020
- Hard
- MCQ
Three solid spheres each of mass \(\mathrm{m}\) and diameter \(d\) are stuck together such that the lines connecting the centres form an equilateral triangle of side of length \(d\). The ratio \(\mathrm{I}_{0} / \mathrm{I}_{\mathrm{A}}\) of moment of inertia \(\mathrm{I}_{0}\) of the system about an axis passing the centroid and about center of any of the spheres \(\mathrm{I}_{\mathrm{A}}\) and perpendicular to the plane of the triangle is
Pick an option to check your answer.
Answer & Solution
Correct Answer
(A) \(\frac{13}{23}\)
Step-by-step Solution
Detailed explanation
From parallel axis theorem
\(I_{0}=3 \times\left[\frac{2}{5} M\left(\frac{d}{2}\right)^{2}+M\left(\frac{d}{\sqrt{3}}\right)^{2}\right]=\frac{13}{10} M d^{2}\)
\(\mathrm{I}_{\mathrm{A}}=\mathrm{I}_{0}+3 \mathrm{M}\left(\frac{\mathrm{d}}{\sqrt{3}}\right)^{2}\)
\(=\frac{13}{10} \mathrm{Md}^{2}+\mathrm{Md}^{2}\)
\(=\frac{23}{10} \mathrm{Md}^{2}\)
\(\frac{\mathrm{I}_{0}}{\mathrm{I}_{\mathrm{A}}}=\frac{13}{23}\)
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