InterviewSolution
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Four thin uniform rods each of length L and massm are joined to form a square. The moment ofinertia of square about an axis along its onediagonal is2mL623(2) m3 mL244 mL3 |
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Answer» We have to use the theorem of parallel axes:I = ICM+Ma2whereICMis the the moment ofinertiaabout an axis through the centre of mass of the rod andIis the moment ofinertiaabout a parallel axis at distancea. The moment ofinertiaof a thin rod of massMand lengthLabout an axis through the mid point of the rod and perpendicular to its length isML2/12. The moment ofinertiaof the rod about a parallel axis at a distanceL/2 (which is the distance of the centre of the frame from each ro.isML2/12 +M(L/2)2=ML2/3 You must remember that moment ofinertiais a scalar quantity. Since there arefourrods in the square frame, the moment ofinertiaof the entire frame is four times the moment ofinertiaof one rod. Therefore Moment of inertia of one partis(4/3)ML2. But diagonals are also mutually perpendicular. Hence ID+ ID= (4/3) ML^2 Hence ID= (2/3) ML^2 |
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