Momentum and CollisionMedium
Question
An open vessel full of water is falling freely under gravity. There is a small hole in one face of the vessel, as shown in the 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 following is correct for the situation described?
Options
A.The value of x is 
B.The value of x is 
C.The value of x can’t be computed from information provided.
D.The question is irrelevant as no water comes out from the hole.
Solution
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
Pinside +
+ ρgeff y = poutside + 
+ ρgeff y
vinside = 0 pinside = poutside = p0 [atmospheric pressure]
Therefore, voutside = 0. i.e., no water comes out.
Pinside +
+ ρgeff y = poutside + + ρgeff y vinside = 0 pinside = poutside = p0 [atmospheric pressure]
Therefore, voutside = 0. i.e., no water comes out.
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