Tag: variation of pressure with depth

Questions Related to variation of pressure with depth

A column of mercure of lenath $h = 10 \mathrm { cm }$ is contained in the middle of a narrow horizontal tube of length $1 \mathrm { m } ,$ closed at both ends. The air in both halves of the tube is under a pressure of $P _ { 0 } = 76 \mathrm { cm }$ of mercury. The tube is now slowly made vertical. The distance moved by mercury will be approximately

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

  1. $4.5$ $\mathrm { cm }$

  2. $3.0$ $\mathrm { cm }$

  3. $2.5$ $\mathrm { cm }$

  4. $1.2$$ $\mathrm { cm }$

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Correct Option: B

The volume of an air bubble increases by $ \mathrm{x} \%  $ as it rises from the bottom of a lake to its surface. If the height of the water barometer is H, the depth of the lake is

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

  1. $

    \left(\dfrac{H+x}{100}\right)^{2}

    $

  2. $

    \dfrac{H x}{(100+x)}

    $

  3. $

    \dfrac{H x}{100}

    $

  4. $

    \dfrac{100 H}{x}

    $

Show answer
Correct Option: C
Explanation:
We have,

$P _1V _1=P _2V _2$

$V _2=V _1+\dfrac{x}{100}V _1$

$P _1V _1=P _2(V _2+\dfrac{x}{100}V _1)$

$P _1=P _2(1+\dfrac{x}{100})$

But,

$P _2=1\,atm$

Then,

$P _1=P _2+\dfrac hH$

$1+\dfrac hH=1+\dfrac{x}{100}$

$h=\dfrac{xH}{100}$

A water tank is 20$\mathrm { m }$ deep. If the waterbarometer reads $10 \mathrm { m } ,$ the pressure at thebottom of the tank is

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

  1. 2 atmosphere

  2. 1 atmosphere

  3. 3 atmosphere

  4. 4 atmosphere

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Correct Option: C

A cylindrical can open at the bottom end lying at the bottom of a lake $47.6\ \text{m}$ deep has $50\ \text{cm}^3$ of air trapped in it. The can is brought to the surface of the lake. The volume of the trapped air will become $($atmospheric pressure $= 70\ \text{cm}$ of Hg and density of Hg $= 13.6\ \text{g/cc)}$:

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

  1. $350\ \text{cm}^3$

  2. $300\ \text{cm}^3$

  3. $250\ \text{cm}^3$

  4. $22\ \text{cm}^3$

Show answer
Correct Option: B
Explanation:

$P _o= 70\ \text{cm}$ of Hg $=70 \times 10^{-2} \times 13600 \times 9.8 =93296\ \text{Pa}$
Using Boyle's law: $P _1V _1 =P _2V _2$
$\Rightarrow (P _o+H \rho g) \times 50 \times 10^{-6}=P _o \times V _2$
$\Rightarrow (93296+47.6 \times 1000 \times 9.8) \times 50 \times 10^{-6}=93296 \times V _2$
$\Rightarrow (93296+466480) \times 50 \times 10^{-6}=93296 \times V _2$
$\Rightarrow V _2 =300 \times 10^{-6}\ \text{m}^3 =300\ \text{cm}^3$

A dam of water reservoir is built thicker at bottom than at the top because

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

  1. pressure of water is very large at the bottom due to its large depth.

  2. water is likely to have more density at the bottom due to its large depth.

  3. quantity of the water at the bottom is very large.

  4. none of the above.

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Correct Option: A
Explanation:

The pressure applied to walls of the dam will be a function of the amount  of water that is over that particular point on the wall. So water pressure is very large at the bottom due to its large depth. That's why dams are constructed thicker at their bottoms than at their tops. So correct option is 'A'.

The height to which a cylindrical vessel be filled with a homogeneous liquid, to make the average force with which the liquid presses the side of the vessel equal to the force exerted by the liquid on the bottom of the vessel, is equal to

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

  1. half of the radius of the vessel

  2. one-fourth of the radius of the vessel

  3. three-fourth of the radius of the vessel

  4. three eight of the radius of the vessel

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Correct Option: A

A tank with a small hole at the bottom has been filled with water and kerosene (specific gravity 0.8). The height of water is 3m and that of kerosene 2m. When the hole is spend the velocity of fluid coming out from it is nearly .(take g=$10ms^{ -2 }$ and density of water = $10^{ 3 }kgm^{ -3 }$)

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

  1. ${ 10.7 }{ ms }^{ -1 }$

  2. ${ 9.8 }{ ms }^{ -1 }$

  3. ${ 8.5 }{ ms }^{ -1 }$

  4. ${ 7.6 }{ ms }^{ -1 }$

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Correct Option: C

A cylindrical tank having cross-sectional area $A$ is filled with water to a height of $2.0m$. A circular hole of cross-sectional area $a$ is opened at a heigh of $75cm$ from the bottom. If $\cfrac{a}{A}=\sqrt{0.2}$, the velocity with which water emerges from the ole is ($g=9.8m{s}^{-2}$)

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

  1. $4.9m{s}^{-1}$

  2. $4.95m{s}^{-1}$

  3. $5.0m{s}^{-1}$

  4. $5.5m{s}^{-1}$

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Correct Option: C

To what height $h$ should a cylindrical vessel of diameter $d$ be filled with a liquid so that due to liquid force on the vertical surface of the vessel be equal to the force on the bottom:

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

  1. $h=d$

  2. $h=2d$

  3. $h=3d$

  4. $h=d/2$

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Correct Option: A

If pressure at half the depth of a lake is equal to $2/3$ pressure at the bottom of the lake then what is the depth of the lake

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

  1. 10m

  2. 20m

  3. 30m

  4. 60m

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Correct Option: B