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' is `I_(s)=I_(x)=(ma^(2))/(2)`
C. The moment of inertia of cube about Z is `I_(s)''=I_(z)+(ma^(2))/(2)`
D. `I_(x)=I_(y)`

Answer

B,D

Explanation

(a) False, because theorem of perpendicular axis is applicable only for plane lamina.
(b) True, because `I_(z)=I_(z)+m((a)/(sqrt2))^(2)=I_(z)+(ma^(2))/(2)`
© False, because z.. is not parallel to z.
(d) True, because X and Y-axes are symmetrical, so `I_(x)=I_(y)`.
The correct options are (b) and (d).