JEE Mains · Physics · STD 11 - 6. system of particles and rotational motion
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
- A \(\frac{13}{23}\)
- B \(\frac{15}{13}\)
- C \(\frac{23}{13}\)
- D \(\frac{13}{15}\)
Answer & Solution
Correct Answer
(A) \(\frac{13}{23}\)
Step-by-step Solution
Detailed explanation
From parallel axis theorem \(I_{0}=3 \times\left[\frac{2}{5} M\left(\frac{d}{2}\right)^{2}+M\left(\frac{d}{\sqrt{3}}\right)^{2}\right]=\frac{13}{10} M d^{2}\) \(\mathrm{I}_{\mathrm{A}}=\mathrm{I}_{0}+3 \mathrm{M}\left(\frac{\mathrm{d}}{\sqrt{3}}\right)^{2}\)…
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