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When two soap bubbles of radii \( a \) and \( b \) \( (b > a) \) coalesce, the radius of curvature of common surface is:

Two narrow bores of diameter \( 5.0 \, \text{mm} \) and \( 8.0 \, \text{mm} \) are joined together to form a U-shaped tube open at both ends. If this U-tube contains water, what is the difference in the level of two limbs of the tube.
[Take surface tension of water \( T = 7.3 \times 10^{-2} \, \text{N m}^{-1} \), angle of contact \( = 0 \), \( g = 10 \, \text{ms}^{-2} \) and density of water \( = 1.0 \times 10^{3} \, \text{kg m}^{-3} \).]

A light cylindrical vessel is kept on a horizontal surface. Area of base is \( A \). A hole of cross-sectional area \( a \) is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impart force of the emerging liquid is \( (a \ll A) \).

Two small drops of mercury each of radius \( R \) coalesce to form a single large drop. The ratio of total surface energy before and after the change is:

Suppose you have taken a dilute solution of oleic acid in such a way that its concentration becomes \( 0.01 \, \mathrm{cm^{3}} \) of oleic acid per \( \mathrm{cm^{3}} \) of the solution. Then you make a thin film of this solution (monomolecular thickness) of area \( 4 \, \mathrm{cm^{2}} \) by considering \( 100 \) spherical drops of radius \( \left( \dfrac{3}{40\pi} \right)^{1/3} \times 10^{-3} \, \mathrm{cm} \). Then the thickness of oleic acid layer will be \( x \times 10^{-14} \, \mathrm{m} \). Where \( x \) is _______.

What will be the nature of flow of water from a circular tap, when its flow rate increased from \( 0.18 \, \text{L/min} \) to \( 0.48 \, \text{L/min} \)? The radius of the tap and viscosity of water are \( 0.5 \, \text{cm} \) and \( 10^{-3} \, \text{Pa s} \), respectively.
(Density of water : \( 10^{3} \, \text{kg/m}^{3} \))

An object is located at \( 2 \, \text{km} \) beneath the surface of the water. If the fractional compression \( \dfrac{\Delta V}{V} \) is \( 1.36\% \), the ratio of hydraulic stress to the corresponding hydraulic strain will be ________.
[Given : density of water is \( 1000 \, \text{kg m}^{-3} \) and \( g = 9.8 \, \text{m s}^{-2} \)]

A soap bubble of radius \( 3 \, \text{cm} \) is formed inside the another soap bubble of radius \( 6 \, \text{cm} \). The radius of an equivalent soap bubble which has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is ________ \( \text{cm} \).

Consider a water tank as shown in the figure. Its cross-sectional area is \( 0.4 \, \text{m}^{2} \). The tank has an opening B near the bottom whose cross-section area is \( 1 \, \text{cm}^{2} \). A load of \( 24 \, \text{kg} \) is applied on the water at the top when the height of the water level is \( 40 \, \text{cm} \) above the bottom, the velocity of water coming out the opening B is \( v \, \text{m s}^{-1} \). The value of \( v \), to the nearest integer, is: [Take value of \( g \) to be \( 10 \, \text{m s}^{-2} \)]

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JEE Main 2021 20th July Evening Shift

Two small drops of mercury each of radius \( R \) coalesce to form a single large drop. The ratio of total surface energy before and after the change is: