A thin metal rod of mass M and length L is into four equal parts by cutting it perpendicular to the length. If moment of inertia of the rod about an axis passing through its centre and perpendicular t

Question

A thin metal rod of mass M and length L is into four equal parts by cutting it perpendicular to the length. If moment of inertia of the rod about an axis passing through its centre and perpendicular to its axis it I , then moment of inertia of each part about the similar axis is

TestHub · Accepted Answer

We know, that moment of inertia has following functional dependence on mass and length of the rod: I ∝ M L 2 If thin rod is split into four equal parts. ​ M ′ = 4 M ​ L ′ = 4 L ​ ∴ I ′ ∝ 4 M ​ ( 16 L 2 ​ ) ⇒ I ′ ∝ 64 M L 2 ​ ⇒ I ′ = 64 I ​ ​

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