Tag: variation of pressure with depth

Questions Related to variation of pressure with depth

If pressure at the half depth of a lake is equal to $\dfrac{3}{4}$ times the pressure at its bottom, then find the depth of the lake . [Take g=$10 m/s^2]$

physics floating bodies pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

  1. $ \dfrac{P _{0}}{\rho g}\ $

  2. $ \dfrac{2P _{0}}{\rho g}\ $

  3. $ \dfrac{P _{0}}{2\rho g}\ $

  4. $ \dfrac{3P _{0}}{\rho g}\ $

Show answer
Correct Option: A
Explanation:
Let depth of the lake be $h$ and pressure at bottom $= P$
Then $P=P _{0}+\rho gh\rightarrow (1)$    $(P _{0}=$ atmospheric pressure, $\rho $ = density of water)
At half depth $(h/2)$ pressure is $\dfrac{3P}{4}$ then :
$\dfrac{3P}{4}=P _{0}+\rho g\dfrac{h}{2}\rightarrow (2)$
On subtracting equation 2 from 1 we get :
$\dfrac{P}{4}=\rho g\dfrac{h}{2}$
$\Rightarrow P=2\rho gh$, substituting this value of $P$ in equation 1:
$2\rho gh=P _{0}+\rho gh$
$\Rightarrow h=\dfrac{P _{0}}{\rho g}\rightarrow $ Depth of the lake

A tank $4m$ high is half filled with water then filled to the top with a liquid of density $0.60 g/cc$ what is the pressure at the bottom of the tank due to these liquids? (take $g=10ms^{-2}$)

physics floating bodies pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

  1. $1.6 \times 10^3Nm^{-2}$

  2. $3.2\times 10^{-3}$

  3. $1.6 \times 10^4Nm^{-2}$

  4. $3.2 \times 10^4Nm^{-2}$

Show answer
Correct Option: C

If the air density were uniform, then the height of the atmosphere above the sea level to produce a normal atmospheric pressure of 1.0 x 10$^{5}$ Pa is(density of air is 1.3 kg/m$^{3}$ , g $=$ 10m/s$^{2}$):

physics floating bodies pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

  1. 0.77 km

  2. 7.7 km

  3. 77 km

  4. 0.077 km

Show answer
Correct Option: B
Explanation:

$\rho g h = 1 \times 10^5$
$\Rightarrow h = \dfrac {10^5}{\rho g} = \dfrac {10^5}{1.3 \times 10} = 7.7 km$

The pressure exerted by a liquid at depth $h$ is given by:

physics floating bodies pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

  1. $\displaystyle \dfrac{h}{dg}$

  2. $hdg$

  3. $\displaystyle \dfrac{h}{d}$

  4. $hg$

Show answer
Correct Option: B
Explanation:

Answer is B.

The pressure exerted by a liquid at a point depends on its vertical depth and density of the liquid only. It is independent of the shape of the container. The pressure at the bottom of the three vessels of different shapes containing the same liquid acts equally in all directions.
Thus, the pressure exerted by the liquid of height $h$ is given as P=hdg, where $h$ is the height, $d$ is the density and $g$ is the acceleration due to gravity.

The pressure exerted by a liquid column of height h is given by (the symbols have their usual meanings).

physics floating bodies pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

  1. $\dfrac {h}{\rho g}$

  2. $h\rho g$

  3. $\dfrac {h}{\rho}$

  4. $hg$

Show answer
Correct Option: B
Explanation:

The pressure exerted by a liquid column of height h is given by-

       $h\rho g$
Since, total mass =$\rho g$
      

State True or False.
A barometric liquid having high density produces a shorter column of liquid.

physics floating bodies pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

Since the pressure by any liquid is proportional to density .

$P=\rho gh$
So  $h=\dfrac{P}{g\rho}$
So from above equation we can say that if the density of fluid is high ,it will produce shorter column .

At a depth of 1000 m in an ocean, what is the absolute pressure? Given density of sea water is $1.03 \times 10^3 kgm^{-3} ,\ g= 10ms^{-2}$

physics floating bodies pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

  1. 104 atm

  2. 100 atm

  3. 108 atm

  4. 110 atm

Show answer
Correct Option: A
Explanation:

Given: $h=1000m  ,  d=1.03\times10^{3}kg/m^{3} ,  g=10m/s^{2}$ 

The absolute pressure is given by: absolute pressure = pressure of water + atmospheric pressure
$P=hdg+1atm=1000\times1.03\times10^{3}\times10+1atm=1.03\times10^{7}Pa+1atm$
$P=103atm+1atm=104atm$

State True or False.
As the vertical height from mean sea level increases, the atmospheric pressure decreases.

physics floating bodies pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

Pressure decreases with increase in altitude. The pressure at any level in the atmosphere may be interpreted as the total weight of the air above a unit area at any elevation. At higher elevations, there are fewer air molecules above a given surface than a similar surface at lower levels.

State True or False.
One atmospheric pressure at sea level is equal to $760\ cm$ of $Hg$.

physics floating bodies pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

  1. True

  2. False

Show answer
Correct Option: B
Explanation:

Wrong statement.

The average air pressure at sea level is equivalent to the pressure produced by a column of water about 10 meters (or about 76 cm of mercury column).
$P=10^5Nm^{-2}$ at sea level
density of mercury is $13600$ $kg m^3$
we know $P=\rho gh$
So $10^{5}=13600\times 9.8\times h$ 
$h=0.76m=76cm$

A bubbles rises from the bottom of a lake $70m$ deep on reaching the surface its volume become (take atmospheric pressure equal to $10m$ of water)

physics floating bodies pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

  1. $4$ times

  2. $2$ times

  3. $10$ times

  4. $3$ times

Show answer
Correct Option: B