An open vessel full of water is falling freely under gravity. There is a small hole in one face of the vessel, was shown in te figure. The water which comes out from the hole at the instant when hole is at height H above the ground strikes the ground at a distance of x from P. Which of the followin is correct for the situation described?
(a). The value of x is `2sqrt((2hH)/(3))`
(b). The value of x is `sqrt((4hH)/(3))`
(c). The value ofx can't be computed from information providec.
(d). The question is irrevalent as no water comes out from the hole.

Answer

D

Explanation

As vessel is falling freely under gravity, the pressure at all points within the liquid remains the same as the atmospheric pressure. If we apply bernoulli's theorem just inside and outside the hole, then
`P_("inside")+(rho_("inside")^(2))/(2)+rhog_(eff)y=P_(outside)+(rhov_(outside)^(2))/(2)+rhog_(eff)y`
`V_("inside")=0,P_("outside")=P_(0)` [atmospheric pressure]
Therefore, `V_("outside")=0` i.e., no water comes out.