1.

The moment of inertia of a hollow cubical box of mass `M` and side `a` about an axis passing through the centres of two opposite faces is equal to.A. `(5 M a^2)/(3)`B. `(5 M a^2)/(6)`C. `(5 M a^2)/(12)`D. `(5 M a^2)/(18)`

Answer» Correct Answer - D
(d) Taking mass of plate `m = (ma^2)/(6) xx 2 = (ma^2)/(3)`
Then `MI` of two plates through which the axis is passing.
`M.I` of `4` plates having symmetrical position from the axis.
=`4 xx[(m a^2)/(12) + m((a)/(2))^2] = 4 xx[(ma^2)/(3)]`
Total `MI = (4 m a^2)/(3) + ( ma^2)/(3) = (5m a^2)/(3)`
using `(M)/(6) = m = MI = (5 M a^2)/(18)`.


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