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Question
With reference to figure of a cube of edge a and mass m, state whether the following are true or false. (O is the centre of the cube.)
- The moment of inertia of cube about z-axis is Iz = Ix + Iy
- The moment of inertia of cube about z ′ is I'z = `I_z + (ma^2)/2`
- The moment of inertia of cube about z″ is = `I_z + (ma^2)/2`
- Ix = Iy
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Solution
a, b and d
Explanation:
a. Theorem of perpendicular axes is applicable only for laminar (plane) objects. Thus. option (a) is false.
b. As z' || z and distance between them = `a sqrt(2)/2 = a/sqrt(2)`
Now, by the 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, the theorem of parallel axis cannot be applied. Thus, option (c) is false.
d. As x and y-axes are symmetrical.
Hence, Ix = Iy
Thus, option (d) is true.
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