Water is flowing continuously from a tap having an internal diameter `8xx10^(-3)`m. The water velocity as it leves the tap is `0.4 ms^(-1)`. The diameter of the water stream at a distance `2xx10^(-1)`m below the tap is close to `(g=10m//s^(2))`

Options

A. `7.5 xx 10 ^(-3)m`
B. `9.6 x 10 ^(-3) m`
C. `3.6 xx 10 ^(-3) m`
D. `5.0 xx 10 ^(-3)m`

Answer

C

Explanation

From Bemoulli.s theorem,
`p _(0) + 1/2 rho v _(1) ^(2) h = P _(0) + 1/2 rho v _(2)^(2) +0`
`v _(2) = sqrt ( v _(1) ^(2) + 2 gh )= sqrt (0.16 + 2 xx 10 xx 0.2) = 2. 03 m//s`
From equation of continuity,` A _(2) v _(2) = A _(1) v _(1)`
`pi (D _(2) ^(2))/( 4) xx v _(2) = pi (D _(1) ^(2))/( 4 ) v _(1) implies D _(2) = D _(1)sqrt ((v _(1))/( v _(2))) = 3. 55 xx 10 ^(-3) m`