A tank of large base area is filled with water up to a height of `5 m`. A hole of `2 cm^(2)` cross section in the bottom allows the water to drain out in continuous streams. For this situation, mark out the correct statement(s) (take `rho_("water")=1000kg//m^(3),g=10ms^(-12))`

Options

A. The cross-sectional area of the emerging stream of water decreases as it falls down.
B. The cross-sectional area of the emerging stream of water increases as it falls down.
C. At a distance of `5 m` below the bottom of the tank, the cross-sectional area of the stream is `1.414 cm^(2)`.
D. At a distance of `5 m` below the bottom of the tank, the cross-sectional area of the stream is `2.86 cm^(2)`.

Answer

A, C

Explanation

Velocity of water is it comes out through the hole is
`v=sqrt(2gh)=sqrt(2xx10xx5)=10m`
From equatioin of continuit `Av=` constant as water falls down, after coming through hole its speed increase and hence `A` decreases. From Bernoulli's theorem
`P_(0)+(rhov^(2))/2+0=p_(0)+(pv_(1)^(2))/2-rhogh`
(just outside hole and `5 m` below the bottom ot tank).
`implies (rhov_(1)^(2))/2=(rhov^(2))/2+rhoghimpliesv_(1)=14.14ms^(-1)`
From `Av=` constant.
`implies2xx10=A_(1)xx14.14impliesA_(1)=1.414cm^(2)`