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Question

Figure shows the variation of the moment of inertia of a uniform rod, about an axis passing through its centre and inclined at an angle θ to the length. The moment of inertia of the rod about an axis passing through one of its ends and making an angle θ=π3 is ( Take the figure to be a part of sine curve)

A
0.45 kg m2
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B
1.8 kg m2
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C
2.4 kg m2
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D
1.5 kg m2
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Solution

The correct option is B 1.8 kg m2
Moment of inertia of rod about an axis passing through centre and making an angle θ is given by

I=ML212sin2θ
Now, from graph maximum I=0.6 when θ=90

0.6=ML212sin(π2)ML2=7.2

Moment of inertia of rod about an axis passing through centre and making an angle θ is given by
I=ML23sin2θ
at θ=π3,I=ML23(34)=ML24=7.24=1.8 kg m2

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