Four solid spheres, each of mass (m) and diameter (d) are stuck together such that the lines joining the centres form a square of side length (d). The ratio of `I_(0)` & `I_(A)` , where `I_(0)` is the moment of inertia of the system about an axis through the centre of the square and `I_(A)` is moment of inertia of the system about the centre of any one of the spheres, is equal to (both axes are perpendicular to plane of paper)

Options

A. `(6)/(11)`
B. `(4)/(11)`
C. `(5)/(11)`
D. `(7)/(11)`

Explanation

`I_(A) = ( 2)/(5)m ((d)/(2))^(2) + 2 x [ ( 2)/( 5)m ((d)/( 2))^(2) + m d^(2)] +[ (2)/( 5) m ((d)/( 2))^(2) + m xx ( sqrt( 2) d)^(2) ] = ( 22)/( 5) md^(2)`
`I_(0) = 4 xx [ (2)/( 5) m ((d)/( 2))^(2) + m ((d)/( sqrt(2)))^(2) ] = (12)/( 5) md^(2) , ` `(I_(0))/( I_(A)) = ((12)/( 5))/( (22)/( 5)) =(6)/( 11)`