Liquid is flowing throgh a tube of nonuniform cross section ratio of the radius at entry a and exit end B of the tube is 3 :2. Then the ratio of velocities at entry A and exit B of liquid is ……

Options

A. `4:9`
B. `9:4`
C. `8:27`
D. `1:1`

Answer

a

Explanation

`(r_(A))/(r_(B))=(3)/(2)`
`(v_(A))/(v_(B))=?`
According to equation of continuity,
`A_(A)v_(A)=A_(B)v_(B)`
`(v_(A))/(v_(B))=(A_(B))/(A_(A))=(pir_(B)^(2))/(pirA^(2))`
`therefore(v_(A))/(v_(B))=((r_(B))/(r_(A)))^(2)=((2)/(3))^(2)`
`(v_(A))/(v_(B))=(4)/(9)`