A non-uniform rod AB of weight w is supported horizontally in a vertical plane by two light strings PA and QB as shown in the figure.G is the centre of gravity of the rod. If PA and QB make angles 30^(@) and 60^(@) respectively with the vertical, the ratio ("AG")/("GB") is

A non-uniform rod AB of weight w is supported horizontally in a vertic

1.	A non-uniform rod AB of weight w is supported horizontally in a vertical plane by two light strings PA and QB as shown in the figure.G is the centre of gravity of the rod. If PA and QB make angles 30^(@) and 60^(@) respectively with the vertical, the ratio ("AG")/("GB") is
Answer» `(1)/(2)` `sqrt(3)` `(1)/(3)` `(1)/(sqrt(3))` SOLUTION :( c) `T_(1) cos 60^(@)=T_(2) sin 60^(@) IMPLIES (T_(1))/(2)=(sqrt(3)T_(2))/(2)` or `T_(1) cos 60^(@)=T_(2) sin 60^(@)` or `T_(1)= sqrt(3)T_(2)`…….(i) `(sqrt(3)T_(1))/(2)xxAG=(T_(2))/(2) XX BG` `therefore (AG)/(BG)=(T_(2))/(sqrt(3)T_(1))` But `(T_(2))/(T_(1))=(1)/(sqrt(3))` [ from Eq. (i)] HENCE, `(AG)/(BG)=(1)/(3)`