A cylindrical vessel contains a liquid of density ρ upto a height h. The liquid is closed by a piston of mass m and area of cross section A. There is a small hole at the bottom of the vessel. The speed with which the liquid comes out of the vessel is

Question

A cylindrical vessel contains a liquid of density ρ upto a height h. The liquid is closed by a piston of mass m and area of cross section A. There is a small hole at the bottom of the vessel. The speed with which the liquid comes out of the vessel is (A) √2gh (B) √2(gh+(mg/ρ A)) (C) √2(gh+(mg/A)) (D) √2gh+(mg/A)

Tardigrade Admin · Accepted Answer

Difference in pressure energy = K.E of the liquid ρ gh + (mg/A) = (1/2) ρ ν2 ; V = √2 ( gh + (mg/ρ A) )

Q. A cylindrical vessel contains a liquid of density $ρ$ upto a height h. The liquid is closed by a piston of mass m and area of cross section A. There is a small hole at the bottom of the vessel. The speed with which the liquid comes out of the vessel is

$2 g h$

$2 (g h + \frac{m g}{ρ A})$

$2 (g h + \frac{m g}{A})$

$2 g h + \frac{m g}{A}$

Difference in pressure energy = K.E of the liquid
$ρ g h + \frac{m g}{A} = \frac{1}{2} ρ ν^{2}; V = 2 (g h + \frac{m g}{ρ A})$

Q. A cylindrical vessel contains a liquid of density ρ upto a height h. The liquid is closed by a piston of mass m and area of cross section A. There is a small hole at the bottom of the vessel. The speed with which the liquid comes out of the vessel is

2gh​

2(gh+ρAmg​)​

2(gh+Amg​)​

2gh+Amg​​