With reference to Fig. of a cube of edge a and mass m, state whether the following are true or false. (O is the centre of the cube.)

Options

A. the moment of inertia of cube about z-axis is `I_(z)=I_(x)+I_(y)`
B. the moment of inertia of cube about z-axis is `I_(z)=I_(z)+(ma^(2))/(2)`
C. the moment of inertia of cube about z''-axis is `I_(z)+(ma^(2))/(2)`
D. `I_(x)=I_(y)`

Answer

a,b,d

Explanation

(a) theorem of perpendicular axces is applicable only for laminer (plane) objects , thus option (a) is false
(B ) As z'|| z and distance between them `a=(sqrt(2))/(2) =(a)/(sqrt(2))`
Now , by theorem of parallel axes
`I_(z)'=I_(z)+m((a)/(sqrt(2)))^(2) =I_(z)+(ma^(2))/(2)`
Hence , choice (B) is true
(C) z'' is not parallel to z hence , throrem of parallel axis connot be applied .
thus option (c ) false .
(d) As x and y -axes aare symmmetrical.
Hence , `I_(x)=I_(y)`
thus , option (d) is true .