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Multiple choice physics fluid pressure pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

A $20$cm long capillary tube is dipped in water. The water rises up to $8$cm. If the entire arrangement is put in a freely falling elevator, the length of water column in the capillary tube will be:

  1. $8$cm

  2. $6$cm

  3. $10$cm

  4. $20$cm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In a freely falling lift, gravitational pull is zero hence the capillary tube will be filled completely.

Multiple choice physics fluid pressure pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

Water rises in a vertical capillary tube upto a length of $10cm.$ If the tube is inclined at $45^o$, the length of water risen in the tube will be,

  1. $10 cm$

  2. $10 \sqrt2 cm$

  3. $\displaystyle \dfrac {10}{\sqrt2}$

  4. none of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The vertical rise in the level of liquid is constant.
Hence for an inclined tube, the effective length is $ \displaystyle\dfrac {h}{\cos\theta} $
So, the length of water risen in the tube will be $ 10 \sqrt 2 cm $

Multiple choice physics pressure in fluids and atmospheric pressure pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

Four identical capillary tubes $a, b, c$ and $d$ are dipped in four beakers containing water with tube ‘$a$’ vertically, tube ‘$b$’ at $30^{o}$, tube ‘$c$’ at $45^{o}$ and tube ‘$d$’ at $60^{o}$ inclination with the vertical. Arrange the lengths of water column in the tubes in descending order.

  1. $d, c, b, a$

  2. $d, a, b, c$

  3. $a, c, d, b$

  4. $a, b, c, d$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In capillary tube fluid always rise to the same vertical height as when the tube is perfectly vertical. So, the tube which is making greater angle with vertical will get more water in it.
So, order of lengths of water column will be $d > c > b > a$.

Multiple choice physics pressure in fluids and atmospheric pressure pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

A capillary tube when immersed vertically in a liquid rises to 3 cm. If the tube is held immersed in the liquid at an angle of 60$^{o}$ with the vertical,the length of the liquid column along the tube will be:

  1. 2 cm

  2. 4.5 cm

  3. 6 cm

  4. 7.5 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation


$h = \dfrac {2T cos \theta}{r \rho g}$
$h \alpha cos \theta$
for $\theta = 60^0 cos \theta = \dfrac {1}{2}$
$\therefore$ h is double $\Rightarrow h = 6 cm$.

Multiple choice physics pressure in fluids and atmospheric pressure pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

A capillary tube is dipped in water vertically.Water rises to a height of 10mm. The tube is now tilted and makes an angle 60$^{o}$ with vertical.Now water rises to a height of:

  1. 10 mm

  2. 5 mm

  3. 20 mm

  4. 40 mm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If capillary tube is tilted the vertical height of water in tube remains same but volume of the water increases in the tube. So, height of water column will be 10mm.

Multiple choice physics pressure in fluids and atmospheric pressure pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

Water rises in a capillary upto a height h. If now this capillary is tilted by an angle of $45^{\circ}$, then the length of the water column in the capillary becomes

  1. 2h

  2. $\displaystyle \frac{h}{2}$

  3. $\displaystyle \frac{h}{\sqrt{2}}$

  4. $h\sqrt{2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The expression for the capillary rise in a tube is given by, 


H = $ \dfrac {2T cos \theta}{\rho g r} $

for all other parameters kept constant, if I change the angle of inclination to $ 45^o $

$ cos \theta $ will go from 1 to $ \dfrac {1}{\sqrt 2} $

Therefore, the height of capillary tube rise will also change from $ H to \dfrac{H}{\sqrt2} $

Multiple choice physics pressure in fluids and atmospheric pressure pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

Two parallel glass plates are dipped partly in a liquid of density $'d'$ keeping them vertical. If the distance between the plates is $'x'$ Surface tension for liquid is $T$ & angle of contact is $\displaystyle \theta $ then rise of liquid between the plates due to capillary will be

  1. $\displaystyle \dfrac{T\cos \theta }{xd}$

  2. $\displaystyle \dfrac{2T\cos \theta }{xdg}$

  3. $\displaystyle \dfrac{2T}{xdg\cos \theta}$

  4. $\displaystyle \dfrac{T\cos \theta }{xdg}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

weight of liquid of height 'h' = (area of tube x h) x g x d= (3.14/4)hdg${x}^2$

vertical component of surface tension force=(1/2)x(Txcircumference)x cosθ=3.14Txcosθ
therefore, (3.14/4)hgd${x}^2$=(1/2)Tx3.14xcosθ
h=(2Tcosθ)/(gdx)
θ
θθs=Tx3.14x

Multiple choice physics pressure in fluids and atmospheric pressure pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

Two capillary tubes of diameters 3.0 mm and 6.0 mm are joined together to form a U-tube open at both ends. If the U-tube is filled with water, what is the difference in its levels in the two limbs of the tube? Surface tension of water at the temperature of the experiment is $7.3 \times 10^{-2} N/m$. Take the angle of contact to be zero and density of water to be $10^3 kg/m^3(g = 9.8 m/s^2)$

  1. 5 mm

  2. 10 mm

  3. 15 mm

  4. 20 mm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\varrho gh=\dfrac { 2T }{ R } $

${ h } _{ 1 }=\dfrac { 2\times 7.3\times { 10 }^{ -2 } }{ { 10 }^{ 3 }\times 9.8\times 1.5\times { 10 }^{ 3 } } $
${ h } _{ 2 }=\dfrac { 2\times 7.3\times { 10 }^{ -2 } }{ { 10 }^{ 3 }\times 9.8\times 3\times { 10 }^{ -3 } } $
So $\triangle h={ h } _{ 1 }-{ h } _{ 2 }$
             $=\dfrac { 2\times 7.3\times { 10 }^{ -2 } }{ { 10 }^{ 3 }\times 9.8\times { 10 }^{ -3 } } \left( \dfrac { 2 }{ 3 } -\dfrac { 1 }{ 3 }  \right) $      
             $=\dfrac { 2\times 7.3\times { 10 }^{ -2 } }{ { 10 }^{ 3 }\times 9.8\times 3\times { 10 }^{ -3 } } $
             $\boxed { \triangle h=5mm } $

Multiple choice physics pressure in fluids and atmospheric pressure pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

Water rises up to a height $h _1$ in a capillary tube of radius $r$. The mass of the water lifted in the capillary tube is $M$. If the radius of the capillary tube is doubled, the mass of water that will rise in the capillary tube will be 

  1. $M$

  2. $2M$

  3. $\cfrac{M}{2}$

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

Since we know that mass of water rise is proportional to volume of water.

Mass $\infty $ volume
$\dfrac { { M } _{ 1 } }{ { M } _{ 2 } } =\dfrac { { V } _{ 1 } }{ { V } _{ 2 } } =\dfrac { \pi { r } _{ 1 }^{ 2 }{ h } _{ 1 } }{ \pi { r } _{ 2 }^{ 2 }{ h } _{ 2 } } =\dfrac { { r } _{ 1 }^{ 2 }{ h } _{ 1 } }{ { r } _{ 2 }^{ 2 }{ h } _{ 2 } } \quad \rightarrow (1)$
and for capillary tube, we know that height $\alpha $ $\dfrac { 1 }{ radius } $
      So, $\dfrac { { h } _{ 1 } }{ { h } _{ 2 } } =\dfrac { { r } _{ 2 } }{ { r } _{ 1 } } \quad \rightarrow (II)$
     hence from (1) & (II)
     $\dfrac { { M } _{ 1 } }{ { M } _{ 2 } } =\dfrac { { r } _{ 1 }^{ 2 } }{ { r } _{ 2 }^{ 2 } } \times \dfrac { { r } _{ 2 } }{ { r } _{ 1 } } =\dfrac { { r } _{ 1 } }{ { r } _{ 2 } } $
     So ${ M } _{ 2 }=\dfrac { { r } _{ 2 } }{ { r } _{ 1 } } \times { M } _{ 1 }=\dfrac { 2r }{ r } \times M=2M$
              $\boxed { { M } _{ 2 }=2M } $

Multiple choice physics pressure in fluids and atmospheric pressure pressure exerted by a liquid column pressure at a certain depth in liquid variation of pressure with depth

In a surface tension experiment with a capillary tube water rises up to $0.1 m$. If the same experiment is repeated on an artificial satellite which is revolving around the earth. The rise of water in a capillary tube will be

  1. $0.1 m$

  2. $9.8 m$

  3. $0.98 m$

  4. Full length of capillary tube
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If the experiment of capillary tube is performed in space then, it will rise to fall length of tube due to vaccum around it, i.e. no external pressure.