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A uniform square plate S (side c) and a ...

A uniform square plate `S (side c)` and a unifrom rectangular plate `R(side b,a)` have identical areas and mass [Fig.]
Show that
(i) `I_(xR)//I_(xS) lt 1`, (ii) `I_(yR)//I_(yS) gt 1`, (iii) `I_(zR)//I_(zS) gt 1`.

A

(i) only

B

(ii) only

C

Both (i) and (ii)

D

Neither (i) nor (ii)

Text Solution

Verified by Experts

The correct Answer is:
c
As, areaof rectangular plate R= Area of square plate S
`therefore a xx b =c^(2)`
i) `(I_(x)R)/(I_(x)S)=b^(2)/c^(2)=b/a`
As `b lt a therefore (I_(x)R)/(I_(x)S) lt 1`
ii) `(I_(y)R)/(I_(y)S) = a^(2)/c^(2)=a/b`
As `a gt b therefore (I_(y)R)/(I_(y)S) gt 1`
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