Imagine a planetary system in which the gravitational force varied as `1/R` instead of `1/R^2`. what relation would correspond to Kepler's third law ( `T^2/R^3`= constant)?

If R is the relation ‘lessthan from A={1,2,3,4,5} to B={1,4,5}. Write down the cartesion product corresponding to R. Also find the inverse relation to R.

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.

Answer carefully: If Coulomb’s law involved 1//r^3 dependence (instead of 1//r^2 ), would Gauss’s law be still true ?

If R_1 and R_2 are equivalence relations in a set A, show that R_1 nn R_2 is also an equivalence relation

If R_1 and R_2 ·are equivalence relations in a set A, show that R_1 nn R_2 is also an equivalence relation.

If R is the relation '' greater than'' for : A = {1, 4, 5,} to B={1,2,4,5,6,7}, write down the elements corresponding to R.

If R is the relation ‘less than' from set A = {1, 2, 3, 4, 5} to B = {1,4,6}. Write down the cartesian product corresponding to R. Also find inverse relation to R.

If R is a relation "is divisor of" from the set A = {1, 2, 3} to B = {4, 10, 15}, write down the set of ordered pairs corresponding to R.