The velocity of water in river is 9 km/h of the upper surface . The river is 10 m deep . If the coefficient of viscosity of water is `10^(-2) ` poise then the shearing stress between horizontal layers of water is

Options

A. `0.25 xx 10^(-2) N// m^(2)`
B. `0.25 xx 10^(-3) N//m^(2)`
C. `0.5 xx 10^(-3) N//m^(2)`
D. `0.75 xx 10^(-3) N//m^(2)`

Answer

A

Explanation

Shearing stress = `(F)/(A)`
and viscous force F = `eta A""(dv)/(dx)`
`therefore ` Shearing stress = `(eta A"" (dv)/(dx))/(A) = eta "" (dv)/(dx)`
`(10^(-2) "poise" [ 9 xx (5)/(18)] m//s)/(10 m) = 0.25 xx 10^(-2) N//m^(2)`