Two tanks contain different liquids, one having density twice that of the other. Holes of cross-section ratio 2 : 1 are made at heights `h_(1)` and `h_(2)` below the levels of liquids in the tank which have same heights from the bottom of the tanks. When mass flux is same, then the ratio of the heights `h_(2)` to `h_(1)` is :

Options

A. 2
B. 4
C. 8
D. 16

Answer

D

Explanation

Mass flux= rate of flow of liquid `xx` density
= area `xx` velocity `xx` density
`thereforem_(1)=a_(1)xxsqrt(2gh_(1))xxp_(1)`
and `m_(2)=a_(2)xxsqrt(2gh_(2))xxp_(2)`
since `m_(1)=m_(2)`
`thereforea_(1)xxsqrt(2gh_(1))xxp_(1)=a_(2)xxsqrt(2gh_(2))xxp-(2)`
`rArr(h_(2))/(h_(1))=((a_(1))/(a_(2)))^(2).((p_(1))/(p_(2)))^(2)`
`(h_(2))/(h_(1))=(2)^(2)xx2^(2)=16`
Thus correct choice is (b).