Artificial satellites go round the earth in their respective orbits. Astronauts are able to float in side the satellite. Inside space of the satellite could be treated as gravity free space. If a beaker filled with a liquid upto height h having a small hole in the bottom is placed in such a satellite, you will wonder te liquid does not come out of the hole. You have to squeeze or force the liquid to come out. suppose a constant pressure p is applied on the liquid through piston to force it out through the hole. Out side pressure could be neglected in comparison with `p` Cross-sectional area of beaker is too greater than that of hole `(Agtgta)`

Options

A. velocity with which liquid comes out of the hole is `sqrt((p)/(rho))`
B. velocity with which liquid comes out of the hole is `sqrt((2p)/(rho))`
C. Time taken to empty the beaker is `(Ah)/(a)sqrt((rho)/(2p))`
D. Time taken to empty the beaker is `(Ah)/(a)sqrt((2rho)/(p))`

Answer

B, C

Explanation

`p=(1)/(2)rhoV^(2)impliesV=sqrt((2p)/(rho))`
`t=(Ah)/(a.v)=(Ah)/(a.sqrt((2p)/(rho)))`