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 uniform square plate S (side c) and a unifrom rectangular plate R(si

1.	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.
Answer» Solution :By givenquestion Area of Squre=Area ofrectangular plate `IMPLIES C^(2)=axxbimpliesc^(2)=ab` Now by defination `(a) (I_(XR))/(I_(xs))=(B^(2))/(c^(2)) ""[:'Iprop(area)^(2)]` from thediagram Bltc `implies (I_(xR))/(I_(xS))=((b^(2))/(c^(2)))lt1impliesI_(xR)ltI_(xs)` (b)`(I_(yR))/(I_(YS))=(a^(2))/(b^(2))` asa gtc `(I_(yR)/(I_(ys))=((a)/(c))^(2)gt1` (c ) `I_(zR)- I_(zs) prop(a^(2)+b^(2)-2c^(2))=a^(2)+b^(2)-2ab=(a-b)^(2) ""[:' C^(2)=ab]` `implies (I_(zR)-I_(zS))gt0impliesI_(zR)/(I_(zs))gt1`