Figure shows a uniform solid block of mass `M` and edge lengths `a, b` and `c`. Its `M.I`. about an axis through one edge and perpendicular (as shown) to the large face of the block is

Options

A. `M/3(a^(2)+b^(2))`
B. `M/4(a^(2)+b^(2))`
C. `(7M)/12(a^(2)+b^(2))`
D. `M/12(a^(2)+b^(2))`

Answer

A

Explanation

`(MI)_(CG)=M((a^2+b^2)/12)`
According to the theorem of parallel axis,
`(MI)_("required axis")=(MI)^(CG)+M(OA)^2`
`=M((a^2+b^2)/3)`