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Four solid spheres, each of mass (m) and...

Four solid spheres, each of mass (m) and diameter (d) are stuck together such that the lines joining the centres form a square of side length (d). The ratio of `I_(0)` & `I_(A)` , where `I_(0)` is the moment of inertia of the system about an axis through the centre of the square and `I_(A)` is moment of inertia of the system about the centre of any one of the spheres, is equal to (both axes are perpendicular to plane of paper)

A

`6/11`

B

`4/11`

C

`5/11`

D

`7/11`

Text Solution

Verified by Experts

The correct Answer is:
A
`I_(A)=2/5m(d/2)^(2)+2xx[2/5m(d/2)^(2)+md^(2)]+[2/5m(d/2)^(2)+md^(2)]+[2/5m(d/2)^(2)+mxx(sqrt(2)d)^(2)]=22/5m^(2)`
`I_(0)=4xx[2/5(d/2)^(2)+m(d/(sqrt(2)))^(2)]=12/5md^(2)" "(I_(0))/(I_(A))=(12/5)/(22/5)=6/11`
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