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A non-uniform rod AB of weight w is supp...

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

`(1)/(2)`

B

`sqrt(3)`

C

`(1)/(3)`

D

`(1)/(sqrt(3))`

Text Solution

Verified by Experts

The correct Answer is:
C
( 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)`
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