Seven identical discs are arranged in a hexagonal, planar pattern so as to touch each neighbor, as shown in the figure. Each disc has mass `m` and radius `r`. What is the moment of inertia of the system of seven discs about an axis passing through the centre of central disc and normal to plane of all discs ?
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Options

A. `(7)/(2) mr^2`
B. `(13)/(2) mr^2`
C. `(29)/(2) mr^2`
D. `(55)/(2) mr^2`

Answer

D

Explanation

(d) `I = I_0 + 6 I'`
`I_0` is the moment of inertia of central disc and `I'` is moment of inertia of rest of the each disc about specified axis.
By parallel axes theorem
`I = (mr^2)/(2) + 6(I_(cm) + md^2) = (mr^2)/(2) + 6[(mr^2)/(2) + m(2 r)^2]`
=`(mr^2)/(2)+(6 mr^2)/(2)+ 24 mr^2 = (55 mr^2)/(2)`.