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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 the side of length d. The ratio \frac{I_O}{I_A} of moment of inertia I0 of the system about an axis passing the centroid and about centre of any of spheres IA and perpendicular to the plane of the triangle is:
Option: 1 \frac{15}{13}
Option: 2  \frac{13}{15}
Option: 3 \frac{13}{23}
Option: 4  \frac{23}{13}
 

Answers (1)

best_answer

As a moment of inertia of one sphere of radius R about its centre= I = \frac{2}{5}mR^2

 

from the figure given it is clear that OC = \frac{d}{\sqrt3}

M.I about O = 3\left[\left(\frac{2}{5}M\left (\frac{d}{2} \right )^2 + M\left(\frac{d}{\sqrt3} \right )^2 \right ) \right ] = \frac{13}{10} Md^2

M.I about A = 2\left[\left (\frac{2}{5}M\left (\frac{d}{2} \right )^2 + M\left(d \right )^2 \right ) \right ] + \frac{2}{5}M\left(\frac{d}{2} \right )^2 = \frac{23}{10} Md^2

New Ratio = \frac{13}{23}

Hence the option correct option is (3).

Posted by

avinash.dongre

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