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Two circular discs A and B have equal ma...

Two circular discs A and B have equal masses and equal thicknesses but have densities `d_(1) and d_(2)` such that `d_(1) gt d_(2)`. Their moments of inertia are related as

A

`I_(1) gt I_(2)`

B

`I_(1) lt I_(2)`

C

`I_(1)=I_(2)`

D

`I_(1) gt gt I_(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
The masses of the discs are equal.
`therefore v_(1)d_(1)=v_(2)d_(2)`
`therefore pir_(1)^(2)hd_(1)=pir_(2)^(2)hd_(2)`
`because` They have the same thickness.
`therefore" "r_(1)^(2)=r_(2)^(2)d_(2)" but "d_(1)gt d_(2)" "therefore" "r_(1)^(2) lt r_(2)^(2)`
But the M.I. of a disc `=(1)/(2)MR^(2)`
`therefore I_(1)=(1)/(2)Mr_(1)^(2) and I_(2)=(1)/(2)Mr_(2)^(2)`
`because r_(1)^(2) lt r_(2)^(2)" "therefore" "I_(1)lt I_(2)`
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