question_answer

To what height water should be filled in a container of height 21 cm, so that it appears as half-filled when viewed from the top \[\left( \text{Take}\,{{\,}_{a}}{{\mu }_{w}}=\frac{4}{3} \right)\]

A)  12 cm                  

B)         15 cm

C)  10.5 cm               

D)         7 cm

Correct Answer: A

Solution :

Let the water should be filled up to height \[x,\] so that bottom of the container should appear to be raised up to height \[(21-x).\] Apparent depth (from figure) \[h=(21-x)\]Real depth, \[h=x\] \[\therefore \]  \[\mu =\frac{h}{h}\] \[\frac{4}{3}=\frac{x}{21-x}\] \[x=12\,cm\] Apparent depth (from figure) \[h=(21-x)\]Real depth, \[h=x\] \[\therefore \]  \[\mu =\frac{h}{h}\]                 \[\frac{4}{3}=\frac{x}{21-x}\] \[x=12\,cm\]