Surface energy, surface tension, angle of contact, excess pressure, drops, bubbles, capillary rise
- 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 ρ and takes a spherical shape of radius R. When the gas is allowed to flow freely out… Answer: 3. a=-1/2,α=-1/2,β=-1,γ=1/2,δ=7/2 Key idea: the excess pressure inside the balloon is proportional to S/r (it is 4S/r in the standar... 1
- 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 ρ, the liquid surface makes angle θ_0(θ_0 1) with the x-axis at x = L.… Answer: 2. d²y/dx²=ρ g/Sy Key idea: the surface tension pulls the curved surface so that, for each small piece, the net vertical force balan... 1
- 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 : Answer: 2. 19.8 mN Key idea: The surface-tension force acts along the line of contact between the disc and the water, which is the circumfer... 1
- 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 N m^-1) Answer: 4. 3.01×10⁻⁴ J A soap bubble has two surfaces (inner and outer), so the energy needed equals surface tension times total area 2×4π r... 1
- If a soap bubble expands, the pressure inside the bubble : Answer: 2. decreases Excess pressure inside a soap bubble is Δ P=4S/r , so it is inversely proportional to the radius. When the bubble expan... 1
- 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 : Answer: 3. 10.0 g Capillary rise: h=2Tcosθ/rρ g , so h∝1/r . Mass of water in the tube m=ρπ r²h∝ r²·1/r=r . Radius doubled gives mass double... 1
- A soap bubble, having radius of 1 mm, is blown from a detergent solution having a surface tension of 2.5×10^-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 w… Answer: 3. 1 cm A soap bubble has two surfaces, so the excess pressure inside is Δ P=4T/R . Δ P=dfrac4×2.5×10⁻²10⁻³=100\ Pa . At depth Z₀ in... 1
- A rectangular film of liquid is extended from (4 cm × 2 cm) to (5 cm × 4 cm). If the work done is 3×10^-4 J, the value of the surface tension of the liquid is Answer: 1. 0.125 N m ⁻¹ Work done in stretching a liquid film is W=T Δ A , where the film has two free surfaces, so Δ A=2×(change in area) .... 1
- Three liquids of densities ρ_1,ρ_2 and ρ_3 (with ρ_1>ρ_2>ρ_3), having the same value of surface tension T, rise to the same height in three identical capillaries. The angles of contact θ_1,θ_2 and θ_3 obey Answer: 1. 0≤θ₁<θ₂<θ₃<π/2 Capillary rise is h=2Tcosθ/rρ g . Here h , T and r are the same for all three liquids, so cosθ∝ρ . Since the liqui... 1