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 μ w =4/3 )

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 μ w =4/3 ) (A) 8.0 cm (B) 10.5 cm (C) 12.0 cm (D) None of the above

Tardigrade Admin · Accepted Answer

To see the container half-filled from top, water should be filled up to height

x

so that bottom of the container should appear to be raised upto height

(21 - x)

.As shown in figure apparent depth

h^{'} = (21 - x)

Real depth

h = x

∴ μ = \frac{h}{h ^{'}} \Rightarrow \frac{4}{3}

= \frac{x}{21 - x} \Rightarrow x = 12 c m

Q. How much water should be filled in a container 21cm in height, so that it appears half filled when viewed from the top of the container? (given that μw​=4/3 )

8.0 cm

10.5 cm

12.0 cm

None of the above

To see the container half-filled from top, water should be filled up to height x so that bottom of the container should appear to be raised upto height (21−x).As shown in figure apparent depth h′=(21−x) Real depth h=x ∴μ=h′h​⇒34​ =21−xx​⇒x=12cm

Q. How much water should be filled in a container $21 c m$ in height, so that it appears half filled when viewed from the top of the container? (given that $μ_{w} = 4/3$ )