Tag: fluids

Questions Related to fluids

In the bottom of a vessel with mercury of density $\rho$ there is a round hole of radius $r$. At what maximum height of the mercury layer will the liquid still not flow out through this hole. (Surface tension = $T$) 

various types of barometer fluids physics

  1. $\dfrac T {rpg}$

  2. $\dfrac T {2rpg}$

  3. $\dfrac {2T} {rpg}$

  4. $\dfrac{4T} {rpg}$

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Correct Option: A
Explanation:

Given,


$r=$ radius of the hole


$p=$ density of mercury liquid

$g=$ acceleration due to gravity

$T=$ Surface tension

$h=$ maximum height

The liquid can not penetrate until the hydro-static pressure is greater than excess pressure.

Limiting condition,

$pgh=\dfrac{2T}{r}$

$h=\dfrac{2T}{rpg}$

The correct option is C.

The height of a mercury barometer is 75 cm at sea level and 50 cm at the top of a hill. Ratio of density of mercury to that of air  is $10 ^ { 4 }$ The height of the hill is

various types of barometer fluids physics

  1. 250 m

  2. 2.5 km

  3. 1 .25 km

  4. 750 m

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Correct Option: C

The brass scale of a barometer gives correct reading at $10^{ o }C$. The barometer reads 75 cm at $30^{ o }C$. What is the atmospheric pressure at $8^{ o }C$(in cm Hg)

various types of barometer fluids physics

  1. 74.8

  2. 75.03

  3. 70

  4. 60

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Correct Option: C

The lengths of air column are 10 and 8 cm in a faulty barometer when it shows 72 and 71 cm. The atmospheric pressure is 

various types of barometer fluids physics

  1. 76 cm of Hg

  2. 75 cm of Hg

  3. 64.4 cm of Hg

  4. None

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Correct Option: C

The height of a mercury barometer is 75$\mathrm { cm }$ at sealevel and 50$\mathrm { cm }$ at the top of a hill. Ratio of density ofmercury to that of air is $10 ^ { * }$ . The height of the hill is 

various types of barometer fluids physics

  1. 250$\mathrm { m }$

  2. 2.5$\mathrm { km }$

  3. 1.25$\mathrm { km }$

  4. 750$\mathrm { m }$

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Correct Option: C

The value of $\mathrm { g }$ at a place decreases by 2$\%$ . The barometric height of mercury 

various types of barometer fluids physics

  1. Increases by 2$\%$

  2. Decreases by 2$\%$

  3. Remains unchanged

  4. Sometimes increases and so

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Correct Option: A

Eight identical spherical mercury drops charged to a potential of $20V$ each are coalesced into a single spherical drop.

various types of barometer fluids physics

  1. The internal Energy of the system remains the same.

  2. The new potential of the drop is $80V$

  3. Internal energy of the system decreases

  4. The potential remains the same i.e., $20V$

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Correct Option: B
Explanation:

Potential of one small drop of mercury, 
$V=\displaystyle\frac{kq}{r}=20V$
Volume of big drop=volume of $8$ small drops
$\displaystyle\frac{4}{3}\pi R^3=8\times \frac{4}{3}\pi r^3\Rightarrow =2r$
$Q'=8q$
Potential of big drop,
$\displaystyle V'=\frac{kQ'}{R}=\frac{K\times 8q}{2r}=\frac{4kq}{r}=4\times 20=80V$
Hence, option $B$ is the correct answer.

A cubical block of steel of each side equal 1 is floating on mercury in vessel. The densities of steel and mercury are $ \rho _s and \rho _m $.The height of the block above the mercury level is given by 

various types of barometer fluids physics

  1. $ I \left( 1+\dfrac { \rho _ s }{ \rho _ m } \right) $

  2. $ I \left( 1-\dfrac { \rho _ s }{ \rho _ m } \right) $

  3. $ I \left( 1+\dfrac { \rho _ m }{ \rho _ s } \right) $

  4. $ I \left( 1-\dfrac { \rho _ m }{ \rho _ s} \right) $

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Correct Option: B

A beaker contining a liquid is kept inside a big closed jar. If the air inside the jar is continuously pumped out, the pressure in the liquid near the bottom of the liquid will

various types of barometer fluids physics

  1. Increase

  2. Decrease

  3. Remain constant

  4. First decrease and then increase

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Correct Option: B

A thin tube of uniform cross - section is sealed at both ends. It lies horizontally, the middle $5 \,cm$ containing mercury and the two equal ends containing air at the same pressure P. When the tube is held at an angle $60^o$ with the vertical, the lengths of the air column above and below the mercury are $46$ and $44.5$ cm respectively. Calculate the pressure P, in cm of Hg. (The temperature of the system is kept at $30$ K)

various types of barometer fluids physics

  1. $92.5$ cm of Hg

  2. $75.4$ cm of Hg

  3. $73.0$ cm of Hg

  4. $70.5$ cm of Hg

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Correct Option: B