Question

A cube of ice floats partly in water and partly in Kerosene oil (fig.). The ratio of the volume of ice immersed in water to that in K.oil is (specific gravity of K.oil is $0.8$ and that of ice is $0.9$)

• A. $1:1$
• B. $1:2$
• C. $2:1$
• D. $4:5$

Answer 1

The correct option is A $1:1$

let the fraction in kerosene be
let the fraction in water be b
and $a+b=1$ ................1
Mathematically depicting the situation,
upward force=downward force
$=0.8akg+bkg=0.9kg$
$0.8a+b=0.9$
$=8a+10b+\mathrm{9..................2}$
From 1 and 2,
$a=b=\frac{1}{2}$
So,
Ratio of volume immersed in kerosene and water$=a:b$
$=\frac{1}{2}:\frac{1}{2}$
$=1:1$