### A glass tumbler having inner depth of 17.5 cm ....

A glass tumbler having inner depth of 17.5 cm is kept on a table. A student starts pouring water $(\mu = 4/3 )$ into it while looking at the surface of water from the above. When he feels that the tumbler is half filled, he stops pouring water. Up to what height, the tumbler is actually filled?

(A) 11.7 cm
(B) 8.75 cm
(C) 7.5 cm
(D) 10 cm

Solution

$\mu = \frac {Real\, Depth}{Apparent\, Depth} = \frac {17.5-y}{y}$

$\therefore \frac {4}{3} = \frac {17.5-y}{y}$

$\therefore y = 7.5 cm$

Real Depth = 17.5 - y = 10 cm