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STD 11 - 6. system of particles and rotational motion — NEET STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceNEETSTD 11 - 6. system of particles and rotational motion4 Marks
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
  • ✓
    $\frac{13}{23}$
  • B
    $\frac{15}{13}$
  • C
    $\frac{23}{13}$
  • D
    $\frac{13}{15}$
✓

Answer

Correct option: A.
$\frac{13}{23}$
a
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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