A thin, light circular loop of diameter \(6\,cm\) rests flat on a surface of a liquid. It is slowly raised upwards by applying a force. When a force of \(0.03\,N\) is applied on it, it just clears the surface of film of the liquid. What is the surface tension of the liquid?
Ans: \(\sigma=0.0796\frac{N}{m}\).
A glass tube of internal radius \(1.5\,cm\) and thickness \(0.5\,cm\) is held vertically with its lower end dipped in water. What is the downward pull on the tube due to the surface tension ? Given: Surface tension of the water is \(0.074\frac{N}{m}\).
Ans: \(F=0.0162N\).
A rectangular frame with cross-piece placed on it is dipped in soap solution and brought out so that a soap film is formed. If the length of the cross-piece is \([3.0\,cm/latex]. What force must be applied on it to keep it on equilibrium. Surface tension of soap solution is [latex]\left(40\times10^{-3}\right)\frac{N}{m}\).
Ans: \(F=\left(2.4\times10^{-3}\right)N\).
A circular ring of radius \(2\,cm\) is dipped in the soap solution so that a soap film is formed. If, by some mechanism, its radius is increased to \(2.5\,cm\) without rupturing the soap film. Find: the amount of work done. Given: Surface tension of the soap film is \(0.03\frac{N}{m}\).
Calculate: the work done in blowing a soap bubble from a radius of \(2\,cm\) to \(3\,cm\). Given: the surface tension of soap is \(30\frac{dyne}{cm}\).
Ans: \(W=3768\,J\).
A liquid drop of diameter D breaks up into n tiny drops of equal diameter. If \(\sigma\)is the surface tension of the liquid. Find: the increase in energy.
Two mercury drops one of radius \(1\,mm\) and other of radius \(2\,mm\) coalesce to form a single drop. Find: the energy released if the surface tension of mercury is \(\left(5.44\times10^{-1}\right)\frac{N}{m}\).
One thousand drops, each of diameter \(10\,nm\) coalesce to forma big drop. Assuming that drops are spherical in shape. Find: the energy liberated . Take: suraface tension of water is \(0.072\frac{N}{m}\).
Ans: \(\left(2.035\times10^{-14}\right)J\).
At high temperature, when glass melts, it has a tendency to change shape into a sphere. Surface tension of glass at \(650^{o}C\) is \(0.3\frac{N}{m}\). At tis temperature, if glass changes from a cylinder of length \(100\,mm\) and radius \(10\,\mu m\), into a sphere. Find: The energy released.
Ans: \(E_{released}=1.74\mu J\).
A thin circular ring of radius \(20\,mm\) and of mass \(\left(7.0\times10^{-4}\right)kg\) is pulled vertically from the surface of water using a sensitive spring of force constant \(0.7\frac{N}{m}\). The spring is in air and an extension of \(3.4\,cm\) is produced in it when the ring just gets free from the surface of the water. Find: the surface tension of water.
Ans: \(\sigma=0.0674\frac{N}{m}\).
The base of the leg of insect is spherical and has a radius of about \(20\mu m\) and its mass is \(3\,mg\). If the insect has \(6\) identical legs and its weight is equally supported by them when sitting on the water surface. Find: The angle \(\theta\) as shown in below figure. Surface tension of the water is \(0.72\frac{N}{m}\).
Ans: \(\theta=57^{o}\).
Water at temperature T has a surface tension \(\sigma\). If \(n\) drops of water each of equal radius \(r\) coalesce at this temperature and form s big drop of radius \(R\). Show that the rise in temperature is \(\frac{3\sigma}{\rho\,C\,J}\left(\frac{1}{r}-\frac{1}{R}\right)\). where \(J\) is in Joule’s conversion factor, \(C\) Specific Heat and \(\rho\) is density of water.
Find: the energy required to break a drop of mercury of radius \(1\,mm\) into \(125\) small droplets of equal radii. Surface tension of mercury is \(540\frac{dyn}{cm}\).
Ans: \(E_{required}=271.3\,J\).
The energy of free surface of a liquid drop is \(5\pi\) times the surface tension of the liquid. Find: The diameter of the drop in C.G.S system.
Ans: \(D=2.24\,cm\).
Two soap bubbles have radii in the ratio \(5:3\). Find: the ratio of the work done to blow the bubbles.
Ans: \(25:9\).
A mercury drop of radius \(5\,mm\) falls from a certain height \(h\) on a flat surface and splits up into \(10^{6}\) drops each of equal radius. If the whole of energy acquired during the fall of drop changes into the surface energy of the droplets. Find: the height \(h\) which the mercury drop falls. Given: Density of the mercury=\(13600\frac{kg}{m^{3}}\) and surface tension \(\sigma=0.465\frac{N}{m}\).
