An ideal fluid through a pipe of circular cross-section made of two sections with diameters `2.5 cm` and `3.75 cm`. The ratio of the velocities in the two pipes is

Options

A. `9:4`
B. `3:2`
C. `sqrt(3):sqrt(2)`
D. `sqrt(2) : sqrt(3)`

Answer

A

Explanation

According to equation of continuity `A_(1)v_(1) = A_(2)v_(2)`
`(v_1)/(v_2) = (A_2)/(A_1) = (pi D_(2)^(2)//4)/(pi D_(1)^(2)//4) = ((D_2)/(D_1))^(2)`
Here, `D_(1) = 2.5 cm, D_(2) = 3.75 cm`
`:. (v_1)/(v_2) = (3.75/2.5)^(2) = (3/2)^(2) = 9/4`.