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Q.

Four identical thin rods each of mass M and length l form a square frame. Moment of inertia of this frame about an axis through the centre of the square and perpendicular to its plane is

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a

43Ml2

b

23Ml2

c

133Ml2

d

13Ml2

answer is A.

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Detailed Solution

The moment of inertia of each rod about an axis through the centre of frame but perpenducular to frame =[its moment of inertia through its centre of mass and perpendicular to rod + (mass of rod) ×(perpendicular distance between two axes)]= Ml212+M(l2)2 = Ml23Moment of inertia of the system = Ml23×4= 43Ml2
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Four identical thin rods each of mass M and length l form a square frame. Moment of inertia of this frame about an axis through the centre of the square and perpendicular to its plane is