Three solid spheres each of mass 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 I0/ IA of moment of inertial I0 of the system about an axis passing the centroid and about center of any of the spheres IA and perpendicular to the plane of the triangle is :

Engineering

Physics

Moment of Inertia

Question

Three solid spheres each of mass 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 I₀/ I_A of moment of inertial I₀ of the system about an axis passing the centroid and about center of any of the spheres I_A and perpendicular to the plane of the triangle is

$\frac{13}{23}$

$\frac{15}{13}$

$\frac{13}{15}$

$\frac{23}{13}$

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$M . I about P ds = 3 [\frac{2}{3} M {(\frac{d}{2})}^{2} + M {(\frac{d}{\sqrt{3}})}^{2}] = \frac{13}{10} {Md}^{2}$

$M . I about B ds = 2 [\frac{2}{5} m {(\frac{d}{2})}^{2} + M {(d)}^{2}] + \frac{2}{5} M {(\frac{d}{2})}^{2} = \frac{23}{10} {Md}^{2}$

$Now ratio = \frac{13}{23}$