Tag: floating bodies

Questions Related to floating bodies

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

The height of a barometer filled with a liquid of density $3.4\ g/cc$ under normal condition is approximately -

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

  1. $8\ m$

  2. $5\ m$

  3. $3\ m$

  4. $1\ m$

Show answer
Correct Option: C
Explanation:

Given,

$\rho =3.4g/cc=3.4\times 10^3 kg/m^3$
$g=9.8m/s^2$
$P=1.01\times 10^5 Pa$
Pressure, $P=\rho gh$
$h=\dfrac{P}{\rho g}=\dfrac{1.01\times 10^5}{3.4\times 10^3\times 9.8}$
$h=3.03m$
The correct option is C.

A barometer tube reads $76 cm$ of mercury, If the tube is gradually inclined at an angle of $60^\circ$ with vertical, keeping the open end immersed in the mercury reservoir, the length of he mercury column will be:

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

  1. $152 \ cm$

  2. $76 \ cm$

  3. $38 \ cm$

  4. $38 \sqrt{3} cm$

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Correct Option: C

A tank full of water has a small hole  at the bottom. If one-fourth of the tank is emptied in $t$ seconds and remaining three-fourths of the tank is emptied in $t _2$ seconds. Then the ratio $\frac{t _1}{t _2}$ is

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

  1. $\sqrt{3}$

  2. $\sqrt{2}$

  3. $\frac{1}{\sqrt{2}}$

  4. $\frac{2}{\sqrt{2}}-1$

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Correct Option: C

A small hole is made at a height of $(1/\sqrt{2})m$ from the bottom of a cylindrical water tank. The length of the water column is $\sqrt{2}m$. Find the distance where the water emerging from the hole strikes the ground.

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

  1. $4m$

  2. $2m$

  3. $3m$

  4. $\sqrt{2}m$

Show answer
Correct Option: C