Water from a tap emerges vertically downwards with iitial velocity `4ms^(-1)`. The cross-sectional area of the tap is A. The flow is steady and pressure is constant thorughout the stream of water. The distance `h` vertically below the tap, where the cross-sectional area of the stream becomes `((2)/(3))A` is `(g=10m//s^(2))`

Options

A. 0.5 m
B. 1 m
C. 1.5 m
D. 2.2 m

Answer

B

Explanation

The equation of continuity
`A_(1)v_(1)=A_(2)v_(2),Axx4=(2)/(3)Axxv_(2)`, from bernoulli's
Theorem `P+rhogh_(1)+(1)/(2)rho_(1)^(2)=P+rhogh_(2)+(1)/(2)rhov_(2)^(2)` or
`g(h_(1)h_(2))=(1)/(2)(v_(2)^(2)-v_(1)^(2))`
`gxxh=(1)/(2)[(6)^(2)-(4)^(2)][becauseh_(1)h_(2)=h]impliesh=1m`