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 $\frac { I _ { 0 } } { I _ { A } }$ of moment of inertia $I _ { 0 }$ 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: (1) $\frac { 13 } { 23 }$ (2) $\frac { 15 } { 13 }$ (3) $\frac { 23 } { 13 }$ (4) $\frac { 13 } { 15 }$
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 $\frac { I _ { 0 } } { I _ { A } }$ of moment of inertia $I _ { 0 }$ 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:\\
(1) $\frac { 13 } { 23 }$\\
(2) $\frac { 15 } { 13 }$\\
(3) $\frac { 23 } { 13 }$\\
(4) $\frac { 13 } { 15 }$