`A` test tube of thin walls has some lead shots in it at its bottom and the system floats vertically in water,sinking by a length `l_(o) = 10cm`. `A` liquid of density less than that of water, is poured into the tube till the levels inside and outside the tube are even. If the tube now sinks to a length `l_(o) = 40cm`, the specific gravity of the liquid is___.

Answer

0.75

Explanation

`mg=A xx l_(0) xx rho_(w)g" "……(1)`
`(mg+Axx4l_(0)xxrho.g)=A4l_(0)rho_(w)g " " ……(2)`
From `(1) & (2)`
`Al_(0)rho_(w)g + A4l_(0)rhog=A4l_(0)rho_(w)g`
`4rho=3rho_(w)`
`(rho)/(rho_(w)) = (3)/(4)`
specific gravity `=0.75`