Question

How much water should be filled in a container 21 cm in height, so that it appears half filled when viewed from the top of the container (given that ${}_a{\mu }_{\omega }=\frac{4}{3}$)

• A. 8.0 cm
• B. 10.5 cm
• C. 12.0 cm
• D. 15.0 cm

Answer 1

The correct option is C

12.0 cm

The total height of the container = 21 cm
Let the depth of the water in the container be x
Then empty part of the container = 21 - x
To see the container half-filled from the top, the bottom of the container should appear to be raised upto height (21–x) from the surface of the liquid.
As shown in figure apparent depth h'=(21 -x)
Real depth h = x

$\therefore \mu =\frac{h}{h^{\prime }}\Rightarrow \frac{4}{3}=\frac{x}{21-x}\Rightarrow x=12cm$