JEE MAIN - Physics (2021 - 24th February Evening Shift - No. 27)
A uniform thin bar of mass 6 kg and length 2.4 meter is bent to make an equilateral hexagon. The moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of hexagon is _______ $$\times$$ 10$$-$$1 kg m2.
Answer
8
Explanation
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MOI of AB about $$P:{I_{ABp}} = {{{M \over 6}{{\left( {{l \over 6}} \right)}^2}} \over {12}}$$
MOI of AB about O,
$${I_{A{B_O}}} = \left[ {{{{M \over 6}{{\left( {{l \over 6}} \right)}^2}} \over {12}} + {M \over 6}{{\left( {{l \over 6}{{\sqrt 3 } \over 2}} \right)}^2}} \right]$$
$${I_{Hexago{n_0}}} = 6{I_{A{B_0}}} = M\left[ {{{{l^2}} \over {12 \times 36}} + {{{l^2}} \over {36}} \times {3 \over 4}} \right]$$
$$ = {6 \over {100}}\left[ {{{24 \times 24} \over {12 \times 36}} + {{24 \times 24} \over {36}} \times {3 \over 4}} \right]$$
= 0.8 kgm2
= 8 $$\times$$ 10$$-$$1 kg-m2
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