If a vessel containing a fluid of density p upto height h is accelerated vertically downwards with acceleration a0. Then the pressure by fluid at the bottom of vessel is given by the equation (P0. denotes the atmospheric pressure and ' g ' denotes the acceleration due to gravity)

Question

If a vessel containing a fluid of density p upto height h is accelerated vertically downwards with acceleration a0. Then the pressure by fluid at the bottom of vessel is given by the equation (P0. denotes the atmospheric pressure and ' g ' denotes the acceleration due to gravity) (A) P=P0+ρ g h+ρ h a0 (B) P=P0+ρ g h (C) P=P0+ρ h(g-a0) (D) P=P0-ρ g h

Tardigrade Admin · Accepted Answer

When a vessel containing a fluid of density

ρ

upto height

h

is accelerated downwards with acceleration

a_{0}

, then net gravitational acceleration acting on the fluid

g^{'} = g - a_{0} \dots .

(i)
Hence, the pressure by the fluid at the bottom of vessel is given as

p = p_{0} + ρ g h = p_{0} + ρ (g - a_{0}) h [

From Eq. (i)

]

$P = P_{0} + ρ g h + ρ h a_{0}$

$P = P_{0} + ρ g h$

$P = P_{0} + ρ h (g - a_{0})$

$P = P_{0} - ρ g h$

Q. If a vessel containing a fluid of density p upto height h is accelerated vertically downwards with acceleration a0​. Then the pressure by fluid at the bottom of vessel is given by the equation ________(P0​ denotes the atmospheric pressure and ' g ' denotes the acceleration due to gravity)

P=P0​+ρgh+ρha0​

P=P0​+ρgh

P=P0​+ρh(g−a0​)

P=P0​−ρgh

$P = P_{0} + ρ g h + ρ h a_{0}$

$P = P_{0} + ρ g h$

$P = P_{0} + ρ h (g - a_{0})$

$P = P_{0} - ρ g h$