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Question

A rectangular lamina of mass 6 kg is placed in such a way that the centre of rectangular lamina coincides with the origin(O) as shown in figure. If Ix and Iy are the moment of inertia of rectangular lamina about x - axis and y - axis respectively, then find the ratio IxIy.

A
1
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B
12
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C
14
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D
34
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Solution

The correct option is C 14

Mass of lamina, m=6 kg
length of rectangular lamina a=4 m
Width of rectangular lamina b=2 m.
MOI of rectangular lamina about x - axis:
Ix=mb212
Ix=6×(2)212=2 kg-m2

Simillarly, MOI of rectangular lamina about y - axis:
Iy=ma212
Iy=6×4212=8 kg-m2
So, the ratio of Ix & Iy,
IxIy=28=14

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