Question

In a vessel of depth $21\text{cm}$, upto what height the water should be filled so that now it appears to be half filled if viewed from the top? $(\text{Take}{\text{n}}_{\text{w}}=\frac{4}{3})$

• A. $22\text{cm}$
• B. $21\text{cm}$
• C. $11\text{cm}$
• D. $12\text{cm}$

Answer 1

The correct option is D $12\text{cm}$

Let the vessel is filled with water upto height $x$ when it appears to be exactly half filled, when viewed from the top. i.e., the depth of the vessel below the water surface seems to be the same as its height above it.

$\text{Apparent depth of water}=\frac{\text{Actual depth of water}}{{\text{n}}_{\text{w}}}\Rightarrow 21-x=\frac{x}{\frac{4}{3}}\Rightarrow (21-x)4=3x\Rightarrow 21\times 4=7x\Rightarrow x=12\text{cm}$