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Q.

Consider an elliptic disc having uniform distribution of mass M as shown in figure. The moment of inertia (M.I.) about the major and minor axis are 14mb2 and 14ma2 respectively. Then

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a

The M.I. about a line, in its plane, passing through its centre and inclined at an angle θ to the major axis is 14m(b2cos2θ+a2sin2θ)

b

The M.I. about a chord of length 2r passing through O and lying in plane of elliptic disc is 14Ma2b2r2

c

The M.I. about a line perpendicular to the plane of elliptic disc and passing through the centre O is  14M(a2+b2)

d

The M.I. about a line, in its plane, passing through its centre and inclined at an angle θ to the minor axis is 14m(b2sin2θ+a2cos2θ)

answer is A, B, C, D.

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Detailed Solution

We know that 
IPQ=Ixcos2θ+Iysin2θIxysin2θIPQ=14mb2cos2θ+14ma2sin2θIxy=0
The equation of ellipse is 
x2a2+y2b2=1
r2a2cos2θ+r2b2sin2θ=1a2sin2θ+b2cos2θ=a2b2r2

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IPQ=14mb2cos2θ+a2sin2θ=14ma2b2r2

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