question_answer

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 \[_{a}{{\mu }_{\omega }}=4/3\])  [MP PMT 1989]

A)            8.0 cm                                     

B)            10.5 cm

C)            12.0 cm                                   

D)            None of the above

Correct Answer: C

Solution :

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