[" 16.Check the correctness of the relation "],[h=(2 sigma cos theta)/(r^(2)dg)" ,where "h" is height,"sigma" is surface "]

Check the correctness of the relation h =(2 sigma cos theta)/(r^2 dg), where h is height , sigam is surface tension, theta is angle of contact, r is radius, d is density and g in acceleration due to gravity.

Test if the following equation is dimensionally correct: h= ((sS cos theta)/(r p g)) where h= height, S= surface tension, p= density, r=radius, and g= acceleration due to gravity.

Find the total number of sigma bonds in H_(n)P_(n)O_(3m), where ngt2 is :

Assertion : Pressure in bubble ( r ) in the atmosphere of pressure P_0 is P_0+(4sigma)/r where r is the radius and sigma is surface tension . Reason: (4sigma)/r is the excess pressure due to two surface exposed to the atmosphere .

Assertion : Pressure in bubble ( r ) in the atmosphere of pressure P_0 is P_0+(4sigma)/r where r is the radius and sigma is surface tension . Reason: (4sigma)/r is the excess pressure due to two surface exposed to the atmosphere .

Suppose the surface charge density over a sphere of radius R depends on a polar angle theta as sigma = sigma_(0)cos theta , where sigma_(0) is a positive constant. Show that such a charge distribution can be represented ~s a result ofa small relative shift of two uniformly · charged balls of radius R whose charges are equal in magnitude and opposite in sign. Resorting to this representation, find the electric field strength vector inside the given sphere. [(sigma_(0))/(3in_(0))]

When an uncharged conducting ball of radius R is placed in an external uniform electric field, a surface charge densityh sigma = sigma_(0) cos theta is induced on the ball's surface charge (here sigma_(0) is a constant, theta is a polar angle). Find the magnitude of the resultant electric force acting on an induced charge of the same sign.

The sum of series Sigma_(r=0)^(r) (-1)^r(n+2r)^2 (where n is even) is

The sum of series Sigma_(r=0)^(r) (-1)^r(n+2r)^2 (where n is even) is