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With reference to Fig. of a cube of edge...

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.)

A

The moment of inertia of cube about `z^(')` is `I_(z)^(') = I_z + (ma^(2))/2`

B

The moment of inertia of cube about `z^('')` is `I_(z)^('')= I_z + (ma^(2))/2`

C

`I_x = I_y`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
As z axis is parallel to `z^(')` axis and distance between them `=(asqrt(2))/(2)= a/sqrt(2)`
By the theoremof parallel axes,
`I_(Z)^(')=I_(Z) + m(a/sqrt(2))^(2)= I_(Z)+(ma^(2))/(2)`
Hence, option (a) is correct.
z and `z^('')` are not parallel axes. Hence, option (b) is incorrect.
By symmetry, `I_(x)= I_(y)`, Hence option (c) is correct.
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