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 \[\left( Tak{{e}_{a}}{{\mu }_{w}}=\frac{4}{3} \right)\]

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, \[h=x\] \[\therefore \]  \[\mu =\frac{h}{h}\]                 \[\frac{4}{3}=\frac{x}{21-x}\] \[x=12\,\,cm\]