The time of oscillation of t of a small drop of a liquid under surface tension depends upon the density d, the radius r and the surface tensions s. Prove dimensionally that `t infty sqrt(dr^3//s)`

What is the work done in blowing a soap bubble of radius r ahnd surface tension S?

An artificial satellite is revolving around a planet fo mass M and radius R, in a circular orbit of radius r. From Kepler's third law about te period fo a satellite around a common central bdy, square of the period of revolution T is proportional to the cube of the radius of the orbit r. Show usingn dimensional analysis, that T = k/R sqrt((r^3)/(g)) , where k is a dimensionless constant and g is acceleration due to gravity.

If r is the radius, S the surface area and V the volume of a spherical bubble, prove that (ii) (dV)/(dS) oo r

Column - I and Column - II contains four emtries each. Entries of Column -I are to be matched with some entries of Column - II . One or more than one entries of Column -I may have the matching with the same entries of Column - II. {:("column-I","column-II"),("(A) Chemisorption","(P) Not specific and decreases with temperature "),("(B) physisorption",(Q) "sepecific and increases with temperature"),("(C) Desorption of a solute on liquid surface","(R) Increases the surface tension of the liquid "),("(D)Adsorption of a solute on a liquid ","(S) Decreases the surface tension of the liquid "):}

The sap in trees, which consists aminly of water in summer, rises in a system of capilaries of radius r = 2.5 xx 10^-5 m. The surface tension of sap is T = 7.28 xx 10^-2 N m^-1 and the angle of contact is 0^@ . Does surface tension alone account for the supply of water to the top of all trees?

A cone has a fixed radius r and a variable height h. Find the rate of change of its curved surface S w.r.t change in the radius.

Fill in the blanks using the word(s) from the list appended with each statement: Surface tension of liquids generally . . . with temperatures ( increases // decreases )

Mercury has an angle of contact equal to 140^@ with soda lime glass. A narrow tube of radius 1.00 mm made of this glass is dipped in a trough containing mercury. By what amount does the mercury dip down in the tube relative to the liquid surface outside ? Surface tension of mercury at the temperature of the experiment is 0.465 N m^-1 . Density of mercury = 13.6xx 10^3 kg m^-3 .

Two medians drawn from the acute angles of a right angled triangle intersect at an angle pi/6dot If the length of the hypotenuse of the triangle is 3u n i t s , then the area of the triangle (in sq. units) is sqrt(3) (b) 3 (c) sqrt(2) (d) 9

If r is the radius, S the surface area and V the volume of a spherical bubble, prove that (i) (dV)/(dt)=4pir^(2)(dr)/(dt)