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How to calculate moment of inertia in these type of problems explain please
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Asked by nipunverma59 | 05 Apr, 2019, 13:10: PM
answered-by-expert Expert Answer
In case-1, all spheres are 25 cm from axis of rotation.
 
By parallel axis theorem, moment of inertia of sphere whose axis of rotation is parallel to axis of sphere = (2/5)MR2 +Md2  .....(1)
 
where M is mass of sphere, R is radius of sphere and d is distance between axis of rotation and axis of sphere.
 
Using eqn.(1), Moment of Inertia I1 of 4 solid spheres for case-1 = 4×[ (2/5)×1×102 ×10-4 + 1×252×10-4 ] = 0.266 kgm2 ............(2)
 
In case-2 two spheres are in axis of roattion and other two spheres are 25√2 cm away from axis of rotation.
 
Hence moment of inertia I2 for case-2  = 2×[ (2/5)×1×102×10-4 ] + 2×[ (2/5)×1×102×10-4 + 1×(25√2)2×10-4 ] = 0.266 kgm2 ..........(3)
 
from (2) and (3), we have  I1 = I2  or  begin mathsize 12px style I subscript 1 over I subscript 2 space equals space 1 end style
Answered by Thiyagarajan K | 05 Apr, 2019, 16:09: PM

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