Every question from past board papers on Surface energy, surface tension, angle of contact, excess pressure, drops, bubbles, capillary rise, newest paper first. Open any question for its full worked answer.
Consider a water tank shown in the figure. It has one wall at \(x = L\) and can be taken to be very wide in the \(z\) direction. When filled with a liquid of surface tension \(S\) and density \(\rho\), the liquid surface makes angle \(\theta_0(\theta_0 \ll 1)\) with the \(x\)-axis at \(x = L\). If \(y(x)\) is the height of the surface then the equation for \(y(x)\) is :
(take \(\theta(x) = \sin\theta(x) = \tan\theta(x) = \frac{dy}{dx}\), \(g\) is the acceleration due to gravity)
A balloon is made of a material of surface tension \(S\) and its inflation outlet (from where gas is filled in it) has small area \(A\). It is filled with a gas of density \(\rho\) and takes a spherical shape of radius \(R\). When the gas is allowed to flow freely out of it, its radius \(r\) changes from \(R\) to 0 (zero) in time \(T\). If the speed \(v(r)\) of gas coming out of the balloon depends on \(r\) as \(r^a\) and \(T \propto S^{\alpha}A^{\beta}\rho^{\gamma}R^{\delta}\) then
A thin flat circular disc of radius 4.5 cm is placed gently over the surface of water. If surface tension of water is 0.07 Nm\(^{-1}\), then the excess force required to take it away from the surface is :
The amount of energy required to form a soap bubble of radius 2 cm from a soap solution is nearly : (surface tension of soap solution \(=0.03\,\mathrm{N\,m^{-1}}\))
If a soap bubble expands, the pressure inside the bubble :
A capillary tube of radius r is immersed in water and water rises in it to a height h. The mass of the water in the capillary is 5 g. Another capillary tube of radius 2r is immersed in water. The mass of water that will rise in this tube is :
A soap bubble, having radius of 1 mm, is blown from a detergent solution having a surface tension of \(2.5\times10^{-2}\) N/m. The pressure inside the bubble equals at a point \(Z_0\) below the free surface of water in a container. Taking \(g = 10\) m/s\(^2\), density of water \(= 10^3\) kg/m\(^3\), the value of \(Z_0\) is :
A rectangular film of liquid is extended from (4 cm \(\times\) 2 cm) to (5 cm \(\times\) 4 cm). If the work done is \(3\times10^{-4}\) J, the value of the surface tension of the liquid is
Three liquids of densities \(\rho_1,\rho_2\) and \(\rho_3\) (with \(\rho_1>\rho_2>\rho_3\)), having the same value of surface tension \(T\), rise to the same height in three identical capillaries. The angles of contact \(\theta_1,\theta_2\) and \(\theta_3\) obey
