A unifrom 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 unifrom square plate `S (side c)` and a unifrom rectangular plate `R

1.	A unifrom 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`.
Answer» As area of square plate `S = area` of rectangular plate `R` `c^(2) = a xx b` Now, by definition (i) `(I_(xR))/(I_(xS)) = (b^(2))/(c^(2))` As `b lt c, (I_(xR))/(I_(xS)) lt 1` (ii) `(I_(yR))/(I_(yS)) = (a^(2))/(c^(2))` As `a gt c, (I_(yR))/(I_(yS)) gt 1`. (iii) `(I_(zR) - I_(zS)) prop (a^(2) + b^(2) - 2c^(2))` `prop (a^(2) + b^(2) - 2 ab)` `prop (a - b)^(2)`, which is + `:. (I_(xR) I_(xS)) gt 0 or (I_(xR))/(I_(xS)) gt 1`

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A unifrom 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`.

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