Surface Tension
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361190 Two narrow tube of diameters ' \(d_{1}\) ' and ' \(d_{2}\) ' are joined together to form a \(U\) tube open at both ends. If \(U\) tube contains water, the difference in water levels in the limbs is ( \(T\) is the surface tension of water, angle of contact \(=\) zero and density of water \(=\rho, g=\) acceleration due to gravity)

1 \(\dfrac{2 T}{\rho g}\left[\dfrac{d_{1}+d_{2}}{d_{1} d_{2}}\right]\)
2 \(\dfrac{4 T}{\rho g}\left[\dfrac{d_{1} d_{2}}{d_{1}+d_{2}}\right]\)
3 \(\dfrac{2 T}{\rho g}\left[\dfrac{d_{2}-d_{1}}{d_{1} d_{2}}\right]\)
4 \(\dfrac{4 T}{\rho g}\left[\dfrac{d_{2}-d_{1}}{d_{1} d_{2}}\right]\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361191 The lower end of a glass capillary tube is dipped in water. Water rises to a height of \(8\;cm\). The tube is then placed such that height of \(4\;cm\) is only above the surface. The height of water column and angle of contact will be.

1 \(2\,cm,\,60^\circ \)
2 \(4\,cm,\,120^\circ \)
3 \(4\,cm,\,60^\circ \)
4 \(2\,cm,\,30^\circ \)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361192 A glass rod of radius \(r_{1}\) is inserted symmetrically into a vertical capillary tube of radius \(r_{2}\) such that their lower ends are at the same level. The arrangement is now dipped in water. The height to which water will rise into the tube will be ( \(s=\) surface tension of water, \(\rho=\) density of water)
supporting img

1 \(\dfrac{2 S}{\left(r_{2}-r_{1}\right) \rho g}\)
2 \(\dfrac{S}{\left(r_{2}-r_{1}\right) \rho g}\)
3 \(\dfrac{2 S}{\left(r_{2}+r_{1}\right) \rho g}\)
4 \(\dfrac{2 S}{\left(r_{2}^{2}+r_{1}^{2}\right) \rho g}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361193 It two glass plates have water between them and are separated by very small distance (see figure), it is very diffucult to pull them apart. It is because the water in between forms cylindrical surface on the side that gives rise to lower pressure in the water in comparison to atmosphere. If the radius of the cylindrical surface is \(R\) and surface tension of water is \(T\) then the pressure in water between the plates is lower by :
supporting img

1 \(\dfrac{T}{4 R}\)
2 \(\dfrac{2 T}{R}\)
3 \(\dfrac{4 T}{R}\)
4 \(\dfrac{T}{R}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361190 Two narrow tube of diameters ' \(d_{1}\) ' and ' \(d_{2}\) ' are joined together to form a \(U\) tube open at both ends. If \(U\) tube contains water, the difference in water levels in the limbs is ( \(T\) is the surface tension of water, angle of contact \(=\) zero and density of water \(=\rho, g=\) acceleration due to gravity)

1 \(\dfrac{2 T}{\rho g}\left[\dfrac{d_{1}+d_{2}}{d_{1} d_{2}}\right]\)
2 \(\dfrac{4 T}{\rho g}\left[\dfrac{d_{1} d_{2}}{d_{1}+d_{2}}\right]\)
3 \(\dfrac{2 T}{\rho g}\left[\dfrac{d_{2}-d_{1}}{d_{1} d_{2}}\right]\)
4 \(\dfrac{4 T}{\rho g}\left[\dfrac{d_{2}-d_{1}}{d_{1} d_{2}}\right]\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361191 The lower end of a glass capillary tube is dipped in water. Water rises to a height of \(8\;cm\). The tube is then placed such that height of \(4\;cm\) is only above the surface. The height of water column and angle of contact will be.

1 \(2\,cm,\,60^\circ \)
2 \(4\,cm,\,120^\circ \)
3 \(4\,cm,\,60^\circ \)
4 \(2\,cm,\,30^\circ \)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361192 A glass rod of radius \(r_{1}\) is inserted symmetrically into a vertical capillary tube of radius \(r_{2}\) such that their lower ends are at the same level. The arrangement is now dipped in water. The height to which water will rise into the tube will be ( \(s=\) surface tension of water, \(\rho=\) density of water)
supporting img

1 \(\dfrac{2 S}{\left(r_{2}-r_{1}\right) \rho g}\)
2 \(\dfrac{S}{\left(r_{2}-r_{1}\right) \rho g}\)
3 \(\dfrac{2 S}{\left(r_{2}+r_{1}\right) \rho g}\)
4 \(\dfrac{2 S}{\left(r_{2}^{2}+r_{1}^{2}\right) \rho g}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361193 It two glass plates have water between them and are separated by very small distance (see figure), it is very diffucult to pull them apart. It is because the water in between forms cylindrical surface on the side that gives rise to lower pressure in the water in comparison to atmosphere. If the radius of the cylindrical surface is \(R\) and surface tension of water is \(T\) then the pressure in water between the plates is lower by :
supporting img

1 \(\dfrac{T}{4 R}\)
2 \(\dfrac{2 T}{R}\)
3 \(\dfrac{4 T}{R}\)
4 \(\dfrac{T}{R}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361190 Two narrow tube of diameters ' \(d_{1}\) ' and ' \(d_{2}\) ' are joined together to form a \(U\) tube open at both ends. If \(U\) tube contains water, the difference in water levels in the limbs is ( \(T\) is the surface tension of water, angle of contact \(=\) zero and density of water \(=\rho, g=\) acceleration due to gravity)

1 \(\dfrac{2 T}{\rho g}\left[\dfrac{d_{1}+d_{2}}{d_{1} d_{2}}\right]\)
2 \(\dfrac{4 T}{\rho g}\left[\dfrac{d_{1} d_{2}}{d_{1}+d_{2}}\right]\)
3 \(\dfrac{2 T}{\rho g}\left[\dfrac{d_{2}-d_{1}}{d_{1} d_{2}}\right]\)
4 \(\dfrac{4 T}{\rho g}\left[\dfrac{d_{2}-d_{1}}{d_{1} d_{2}}\right]\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361191 The lower end of a glass capillary tube is dipped in water. Water rises to a height of \(8\;cm\). The tube is then placed such that height of \(4\;cm\) is only above the surface. The height of water column and angle of contact will be.

1 \(2\,cm,\,60^\circ \)
2 \(4\,cm,\,120^\circ \)
3 \(4\,cm,\,60^\circ \)
4 \(2\,cm,\,30^\circ \)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361192 A glass rod of radius \(r_{1}\) is inserted symmetrically into a vertical capillary tube of radius \(r_{2}\) such that their lower ends are at the same level. The arrangement is now dipped in water. The height to which water will rise into the tube will be ( \(s=\) surface tension of water, \(\rho=\) density of water)
supporting img

1 \(\dfrac{2 S}{\left(r_{2}-r_{1}\right) \rho g}\)
2 \(\dfrac{S}{\left(r_{2}-r_{1}\right) \rho g}\)
3 \(\dfrac{2 S}{\left(r_{2}+r_{1}\right) \rho g}\)
4 \(\dfrac{2 S}{\left(r_{2}^{2}+r_{1}^{2}\right) \rho g}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361193 It two glass plates have water between them and are separated by very small distance (see figure), it is very diffucult to pull them apart. It is because the water in between forms cylindrical surface on the side that gives rise to lower pressure in the water in comparison to atmosphere. If the radius of the cylindrical surface is \(R\) and surface tension of water is \(T\) then the pressure in water between the plates is lower by :
supporting img

1 \(\dfrac{T}{4 R}\)
2 \(\dfrac{2 T}{R}\)
3 \(\dfrac{4 T}{R}\)
4 \(\dfrac{T}{R}\)
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PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361190 Two narrow tube of diameters ' \(d_{1}\) ' and ' \(d_{2}\) ' are joined together to form a \(U\) tube open at both ends. If \(U\) tube contains water, the difference in water levels in the limbs is ( \(T\) is the surface tension of water, angle of contact \(=\) zero and density of water \(=\rho, g=\) acceleration due to gravity)

1 \(\dfrac{2 T}{\rho g}\left[\dfrac{d_{1}+d_{2}}{d_{1} d_{2}}\right]\)
2 \(\dfrac{4 T}{\rho g}\left[\dfrac{d_{1} d_{2}}{d_{1}+d_{2}}\right]\)
3 \(\dfrac{2 T}{\rho g}\left[\dfrac{d_{2}-d_{1}}{d_{1} d_{2}}\right]\)
4 \(\dfrac{4 T}{\rho g}\left[\dfrac{d_{2}-d_{1}}{d_{1} d_{2}}\right]\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361191 The lower end of a glass capillary tube is dipped in water. Water rises to a height of \(8\;cm\). The tube is then placed such that height of \(4\;cm\) is only above the surface. The height of water column and angle of contact will be.

1 \(2\,cm,\,60^\circ \)
2 \(4\,cm,\,120^\circ \)
3 \(4\,cm,\,60^\circ \)
4 \(2\,cm,\,30^\circ \)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361192 A glass rod of radius \(r_{1}\) is inserted symmetrically into a vertical capillary tube of radius \(r_{2}\) such that their lower ends are at the same level. The arrangement is now dipped in water. The height to which water will rise into the tube will be ( \(s=\) surface tension of water, \(\rho=\) density of water)
supporting img

1 \(\dfrac{2 S}{\left(r_{2}-r_{1}\right) \rho g}\)
2 \(\dfrac{S}{\left(r_{2}-r_{1}\right) \rho g}\)
3 \(\dfrac{2 S}{\left(r_{2}+r_{1}\right) \rho g}\)
4 \(\dfrac{2 S}{\left(r_{2}^{2}+r_{1}^{2}\right) \rho g}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361193 It two glass plates have water between them and are separated by very small distance (see figure), it is very diffucult to pull them apart. It is because the water in between forms cylindrical surface on the side that gives rise to lower pressure in the water in comparison to atmosphere. If the radius of the cylindrical surface is \(R\) and surface tension of water is \(T\) then the pressure in water between the plates is lower by :
supporting img

1 \(\dfrac{T}{4 R}\)
2 \(\dfrac{2 T}{R}\)
3 \(\dfrac{4 T}{R}\)
4 \(\dfrac{T}{R}\)