Tag: fluids

Quizzes (14) Questions (63)

Questions Related to fluids

Multiple choice various types of barometer fluids physics

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 = $T$) 

  1. $\dfrac T {rpg}$
  2. $\dfrac T {2rpg}$
  3. $\dfrac {2T} {rpg}$
  4. $\dfrac{4T} {rpg}$
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

Multiple choice various types of barometer fluids physics

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

  1. 250 m

  2. 2.5 km

  3. 1 .25 km

  4. 750 m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The change in pressure between the sea level and the top of the hill is given by the difference in mercury column heights, which is 75 cm minus 50 cm equals 25 cm of Hg. Using the hydrostatic pressure relation, density of mercury times gravity times height difference equals density of air times gravity times height of the hill. Given the density ratio of mercury to air is 10 to the 4th power, multiplying the mercury column height difference by this ratio yields the height of the hill in meters.

Multiple choice various types of barometer fluids physics

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)

  1. 74.8

  2. 75.03

  3. 70

  4. 60
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The apparent reading of the barometer changes due to the thermal expansion of both the mercury and the brass scale. By correcting for the volume expansion of mercury and the linear expansion of the brass scale, the true pressure at 30 degrees Celsius can be converted to find the pressure at the reference temperature, yielding 75.03 cm of Hg.

Multiple choice various types of barometer fluids physics

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 

  1. 76 cm of Hg

  2. 75 cm of Hg

  3. 64.4 cm of Hg

  4. None
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In a faulty barometer with trapped air, the true atmospheric pressure P equals the sum of the mercury reading h and the pressure due to the trapped air p, so P times the volume is constant according to Boyle's law (P - h1) times l1 equals (P - h2) times l2. Substituting the given values allows solving for the actual atmospheric pressure.

Multiple choice various types of barometer fluids physics

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 

  1. 250$\mathrm { m }$
  2. 2.5$\mathrm { km }$
  3. 1.25$\mathrm { km }$
  4. 750$\mathrm { m }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice various types of barometer fluids physics

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

  1. Increases by 2$\%$
  2. Decreases by 2$\%$

  3. Remains unchanged

  4. Sometimes increases and so
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Barometric height h = P / (rho * g). If P is constant and rho is constant, h is inversely proportional to g. If g decreases by 2%, h must increase by approximately 2%.

Multiple choice various types of barometer fluids physics

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

  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., $20V$
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

Multiple choice various types of barometer fluids physics

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 

  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) $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

By Archimedes' principle, the weight of the block equals the weight of the displaced mercury. rho_s * L^3 * g = rho_m * (L^2 * (L-h)) * g, where h is the height above the surface. rho_s * L = rho_m * (L-h). L - h = L * (rho_s / rho_m). h = L * (1 - rho_s / rho_m).

Multiple choice various types of barometer fluids physics

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

  1. Increase

  2. Decrease

  3. Remain constant

  4. First decrease and then increase
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The pressure at depth h in a liquid is P = P_atm + rho * g * h. If the air is pumped out, P_atm decreases, so the total pressure at any depth h also decreases.

Multiple choice various types of barometer fluids physics

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)

  1. $92.5$ cm of Hg
  2. $75.4$ cm of Hg
  3. $73.0$ cm of Hg
  4. $70.5$ cm of Hg
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the ideal gas law PV=nRT and the condition that the mercury column is in equilibrium, the pressure P can be determined by balancing forces at the given angle. The change in air column lengths due to the shift in mercury position allows for solving the system of equations for P. The calculated value aligns with 75.4 cm of Hg.