Question

Four balls of radius 10cm and mass 1kg,2kg,3kg and 4kg are attached to the periphery of massless plate of radius 1m.What is the moment of inertia of the plate? ​

Answer 1

Answer:

moment of inertia about AB is 7 kgm² and radius of gyration is √(0.7) m

there are four point masses 1kg, 2kg, 3kg and 4kg are located at the corners A, B , C and D respectively of a square ABCD of side 1m as shown in figure.

now momentum of inertis about AB , I =

= (1kg)(0)² + (2kg)(0)² + (3kg)(1m)² + (4kg)(1m)²

= 0 + 0 + 3 kgm² + 4kgm²

= 7 kgm²

now let radius of gyration is r

so, (1 kg + 2kg + 3kg + 4kg)r² = I = 7kgm²

⇒10r² = 7

⇒r = √(0.7) m

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