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A solid sphere of mass M and radius R is...

A solid sphere of mass M and radius R is divided into two unequal parts. The first part has a mass of `(7M)/(8)` and is converted into a uniform disc of radius 2R. The second part is converted into a uniform solid sphere. Let `I_(1)` be the moment of inertia of the disc about its axis and `I_(2)` be the moment of inertia of the new sphere about its axis. The ratio `(I_(1))/(I_(2))` is equal to __________ .

Text Solution

Verified by Experts

The correct Answer is:
140
`I_(1) = (7M)/(8) xx ((2R)^(2))/(2) = (7)/(4) MR^(2)`
`I_(2) = (2)/(5) xx ((M)/(8)) xx ((R)/(2))^(2)` (Radius of new sphere `= (R)/(2)`) `= (1)/(80) MR^(2)`
`I_(1) : I_(2) = 140`
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