Surface Tension
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361241 An air bubble of radius \(r\) in water is at a depth \(h\) below the water surface at some instant. If \(P\) is atmospheric pressure, \(d\) and \(T\) are density and surface tension of water respectively, the pressure inside the bubble will be :

1 \(P+h d g-\dfrac{4 T}{r}\)
2 \(P+h d g+\dfrac{2 T}{r}\)
3 \(P+h d g-\dfrac{2 T}{r}\)
4 \(P+h d g+\dfrac{4 T}{r}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361242 A bubble having surface tension \(T\) and radius \(R\) is formed on ring of radius \(r(r \ll R)\). Air of density \(\rho\) is blown inside the tube with velocity \(v\) such that air molecule collides perpendicularly with the wall of the bubble and stops. The radius at which the bubble separates from the ring is \(\frac{{ZT}}{{\rho {v^2}}}.\) Find \(Z\).

1 2
2 7
3 4
4 9
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361243 The adjoining diagram shows three soap bubbles \(A\), \(B\) and \(C\) prepared by blowing the capillary tube fitted with stop clock \(S, S_{1}, S_{2}\) and \(S_{3}\). With stop clock \(S\) closed and stop clock \(S_{1}, S_{2}\) and \(S_{3}\) opened:
supporting img

1 \(B\) will be start collapsing with volumes of \(A\) and \(C\) increasing
2 \(C\) will start collapsing with volumes of \(A\) and \(B\) increasing
3 \(C\) and \(A\) will both start collapsing with the volume of \(B\) increasing
4 Volumes of \(A\), \(B\) and \(C\) will become equal at equilibrium
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361244 A capillary tube is immersed vertically in water and the height of the water column is \(x\). When this arrangement is taken into a mine of depth \(d\), the height of the water column is \(y\). If \(R\) is the radius of earth, the ratio \(\dfrac{x}{y}\) is :

1 \(\left( {1 - \frac{{2d}}{R}} \right)\)
2 \(\left( {1 - \frac{d}{R}} \right)\)
3 \(\left( {\frac{{R - d}}{{R + d}}} \right)\)
4 \(\left( {\frac{{R + d}}{{R - d}}} \right)\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361245 The radius of spherical drop of water is \(1\;mm\). If surface tension of water be \(70 \times {10^{ - 3}}N{m^{ - 1}}\), the pressure difference inside and outside the drop will be

1 \(70\,N{m^{ - 2}}\)
2 \(140\,N{m^{ - 2}}\)
3 \(280\,N{m^{ - 2}}\)
4 Zero
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361241 An air bubble of radius \(r\) in water is at a depth \(h\) below the water surface at some instant. If \(P\) is atmospheric pressure, \(d\) and \(T\) are density and surface tension of water respectively, the pressure inside the bubble will be :

1 \(P+h d g-\dfrac{4 T}{r}\)
2 \(P+h d g+\dfrac{2 T}{r}\)
3 \(P+h d g-\dfrac{2 T}{r}\)
4 \(P+h d g+\dfrac{4 T}{r}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361242 A bubble having surface tension \(T\) and radius \(R\) is formed on ring of radius \(r(r \ll R)\). Air of density \(\rho\) is blown inside the tube with velocity \(v\) such that air molecule collides perpendicularly with the wall of the bubble and stops. The radius at which the bubble separates from the ring is \(\frac{{ZT}}{{\rho {v^2}}}.\) Find \(Z\).

1 2
2 7
3 4
4 9
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361243 The adjoining diagram shows three soap bubbles \(A\), \(B\) and \(C\) prepared by blowing the capillary tube fitted with stop clock \(S, S_{1}, S_{2}\) and \(S_{3}\). With stop clock \(S\) closed and stop clock \(S_{1}, S_{2}\) and \(S_{3}\) opened:
supporting img

1 \(B\) will be start collapsing with volumes of \(A\) and \(C\) increasing
2 \(C\) will start collapsing with volumes of \(A\) and \(B\) increasing
3 \(C\) and \(A\) will both start collapsing with the volume of \(B\) increasing
4 Volumes of \(A\), \(B\) and \(C\) will become equal at equilibrium
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361244 A capillary tube is immersed vertically in water and the height of the water column is \(x\). When this arrangement is taken into a mine of depth \(d\), the height of the water column is \(y\). If \(R\) is the radius of earth, the ratio \(\dfrac{x}{y}\) is :

1 \(\left( {1 - \frac{{2d}}{R}} \right)\)
2 \(\left( {1 - \frac{d}{R}} \right)\)
3 \(\left( {\frac{{R - d}}{{R + d}}} \right)\)
4 \(\left( {\frac{{R + d}}{{R - d}}} \right)\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361245 The radius of spherical drop of water is \(1\;mm\). If surface tension of water be \(70 \times {10^{ - 3}}N{m^{ - 1}}\), the pressure difference inside and outside the drop will be

1 \(70\,N{m^{ - 2}}\)
2 \(140\,N{m^{ - 2}}\)
3 \(280\,N{m^{ - 2}}\)
4 Zero
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361241 An air bubble of radius \(r\) in water is at a depth \(h\) below the water surface at some instant. If \(P\) is atmospheric pressure, \(d\) and \(T\) are density and surface tension of water respectively, the pressure inside the bubble will be :

1 \(P+h d g-\dfrac{4 T}{r}\)
2 \(P+h d g+\dfrac{2 T}{r}\)
3 \(P+h d g-\dfrac{2 T}{r}\)
4 \(P+h d g+\dfrac{4 T}{r}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361242 A bubble having surface tension \(T\) and radius \(R\) is formed on ring of radius \(r(r \ll R)\). Air of density \(\rho\) is blown inside the tube with velocity \(v\) such that air molecule collides perpendicularly with the wall of the bubble and stops. The radius at which the bubble separates from the ring is \(\frac{{ZT}}{{\rho {v^2}}}.\) Find \(Z\).

1 2
2 7
3 4
4 9
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361243 The adjoining diagram shows three soap bubbles \(A\), \(B\) and \(C\) prepared by blowing the capillary tube fitted with stop clock \(S, S_{1}, S_{2}\) and \(S_{3}\). With stop clock \(S\) closed and stop clock \(S_{1}, S_{2}\) and \(S_{3}\) opened:
supporting img

1 \(B\) will be start collapsing with volumes of \(A\) and \(C\) increasing
2 \(C\) will start collapsing with volumes of \(A\) and \(B\) increasing
3 \(C\) and \(A\) will both start collapsing with the volume of \(B\) increasing
4 Volumes of \(A\), \(B\) and \(C\) will become equal at equilibrium
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361244 A capillary tube is immersed vertically in water and the height of the water column is \(x\). When this arrangement is taken into a mine of depth \(d\), the height of the water column is \(y\). If \(R\) is the radius of earth, the ratio \(\dfrac{x}{y}\) is :

1 \(\left( {1 - \frac{{2d}}{R}} \right)\)
2 \(\left( {1 - \frac{d}{R}} \right)\)
3 \(\left( {\frac{{R - d}}{{R + d}}} \right)\)
4 \(\left( {\frac{{R + d}}{{R - d}}} \right)\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361245 The radius of spherical drop of water is \(1\;mm\). If surface tension of water be \(70 \times {10^{ - 3}}N{m^{ - 1}}\), the pressure difference inside and outside the drop will be

1 \(70\,N{m^{ - 2}}\)
2 \(140\,N{m^{ - 2}}\)
3 \(280\,N{m^{ - 2}}\)
4 Zero
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361241 An air bubble of radius \(r\) in water is at a depth \(h\) below the water surface at some instant. If \(P\) is atmospheric pressure, \(d\) and \(T\) are density and surface tension of water respectively, the pressure inside the bubble will be :

1 \(P+h d g-\dfrac{4 T}{r}\)
2 \(P+h d g+\dfrac{2 T}{r}\)
3 \(P+h d g-\dfrac{2 T}{r}\)
4 \(P+h d g+\dfrac{4 T}{r}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361242 A bubble having surface tension \(T\) and radius \(R\) is formed on ring of radius \(r(r \ll R)\). Air of density \(\rho\) is blown inside the tube with velocity \(v\) such that air molecule collides perpendicularly with the wall of the bubble and stops. The radius at which the bubble separates from the ring is \(\frac{{ZT}}{{\rho {v^2}}}.\) Find \(Z\).

1 2
2 7
3 4
4 9
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361243 The adjoining diagram shows three soap bubbles \(A\), \(B\) and \(C\) prepared by blowing the capillary tube fitted with stop clock \(S, S_{1}, S_{2}\) and \(S_{3}\). With stop clock \(S\) closed and stop clock \(S_{1}, S_{2}\) and \(S_{3}\) opened:
supporting img

1 \(B\) will be start collapsing with volumes of \(A\) and \(C\) increasing
2 \(C\) will start collapsing with volumes of \(A\) and \(B\) increasing
3 \(C\) and \(A\) will both start collapsing with the volume of \(B\) increasing
4 Volumes of \(A\), \(B\) and \(C\) will become equal at equilibrium
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361244 A capillary tube is immersed vertically in water and the height of the water column is \(x\). When this arrangement is taken into a mine of depth \(d\), the height of the water column is \(y\). If \(R\) is the radius of earth, the ratio \(\dfrac{x}{y}\) is :

1 \(\left( {1 - \frac{{2d}}{R}} \right)\)
2 \(\left( {1 - \frac{d}{R}} \right)\)
3 \(\left( {\frac{{R - d}}{{R + d}}} \right)\)
4 \(\left( {\frac{{R + d}}{{R - d}}} \right)\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361245 The radius of spherical drop of water is \(1\;mm\). If surface tension of water be \(70 \times {10^{ - 3}}N{m^{ - 1}}\), the pressure difference inside and outside the drop will be

1 \(70\,N{m^{ - 2}}\)
2 \(140\,N{m^{ - 2}}\)
3 \(280\,N{m^{ - 2}}\)
4 Zero
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361241 An air bubble of radius \(r\) in water is at a depth \(h\) below the water surface at some instant. If \(P\) is atmospheric pressure, \(d\) and \(T\) are density and surface tension of water respectively, the pressure inside the bubble will be :

1 \(P+h d g-\dfrac{4 T}{r}\)
2 \(P+h d g+\dfrac{2 T}{r}\)
3 \(P+h d g-\dfrac{2 T}{r}\)
4 \(P+h d g+\dfrac{4 T}{r}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361242 A bubble having surface tension \(T\) and radius \(R\) is formed on ring of radius \(r(r \ll R)\). Air of density \(\rho\) is blown inside the tube with velocity \(v\) such that air molecule collides perpendicularly with the wall of the bubble and stops. The radius at which the bubble separates from the ring is \(\frac{{ZT}}{{\rho {v^2}}}.\) Find \(Z\).

1 2
2 7
3 4
4 9
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361243 The adjoining diagram shows three soap bubbles \(A\), \(B\) and \(C\) prepared by blowing the capillary tube fitted with stop clock \(S, S_{1}, S_{2}\) and \(S_{3}\). With stop clock \(S\) closed and stop clock \(S_{1}, S_{2}\) and \(S_{3}\) opened:
supporting img

1 \(B\) will be start collapsing with volumes of \(A\) and \(C\) increasing
2 \(C\) will start collapsing with volumes of \(A\) and \(B\) increasing
3 \(C\) and \(A\) will both start collapsing with the volume of \(B\) increasing
4 Volumes of \(A\), \(B\) and \(C\) will become equal at equilibrium
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361244 A capillary tube is immersed vertically in water and the height of the water column is \(x\). When this arrangement is taken into a mine of depth \(d\), the height of the water column is \(y\). If \(R\) is the radius of earth, the ratio \(\dfrac{x}{y}\) is :

1 \(\left( {1 - \frac{{2d}}{R}} \right)\)
2 \(\left( {1 - \frac{d}{R}} \right)\)
3 \(\left( {\frac{{R - d}}{{R + d}}} \right)\)
4 \(\left( {\frac{{R + d}}{{R - d}}} \right)\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361245 The radius of spherical drop of water is \(1\;mm\). If surface tension of water be \(70 \times {10^{ - 3}}N{m^{ - 1}}\), the pressure difference inside and outside the drop will be

1 \(70\,N{m^{ - 2}}\)
2 \(140\,N{m^{ - 2}}\)
3 \(280\,N{m^{ - 2}}\)
4 Zero