Weighing the earth:You are given the following data :`g=9.81 m s^(-2) ,R_E = 6.37 xx 10 ^6 m`, the distance to the mooon `R = 3.84 xx 10^8 m` and the time period of moon's revoluti8n is 27.3 days.Obtain the mass of the earth `M_E` in two different ways.

If p_0 = 1.03 xx 10^5 N m^-2, rho_0 = 1.29 kg m^-3 and g = 9.8 m s^-2 , at what height will the pressure drop to (1/10) the value at the surface of the earth?

Find the mass of earth (Given the radius of earth R= 6.4 xx 10^6 m) .

The mass to charge ratio (m//e) for a cation is 1.5xx10^(-8) kg//C. What is the mass of this cation?

If mass of Earth is 6xx10^24 kg, radius of Earth is 6.4 xx 10^6m and the gravitational constant is 6.7 xx10^-(11)Nm^2kg(-2) . Calculate the value of g.

The velocity of an e in excited state of H-atom is 1.093 xx 10^(6)m//s , what is the circumference of this orbit?

The acceleration due to gravity on the surface of moon is 1.7 m s^-2 . What isthe time period of a simple pendulum on the surface of moon if itstime period on the surface of earth is 3.5 s? (gon the surface of earth is 9.8 m s6-2 )

There is another useful system of units, besides the SI/MKS. A system, called the cgs system. In this system Coulumb's law is given by vecF = (Qq)/(r^2) hatr where the distance r is measured in cm (=10^(-2) m) , F in dynes (= 10^(-5) N) and the charges in electrostatic units (es units), where 1es unit of charge = 1/[3] xx 10^(-9) C . The number [3] actually arises the speed of light in vacuum which now taken to be exactly given by c = 2.99792458 xx 10^8 m/s . An approximate value of c then is c = [3] xx 10^8 m/s . Show that the Coulomb law in cgs units yields. 1 esu of charge = 1 (dy )^(1/2) cm . obtain the dimension of units of charge in terms of mass M, length L and time T. show that it is given in terms of fractional powers of M and L.

A magnet weighs 75 g and its magnetic moment is 2xx10^-4 A m^2 . If the density of the material of the magnet is 7.5 xx 10^3 kg m^-3 , calculate the intensity of magnetisation.

Find out the vlaue of 1 Bohr magneton. Givne h = 6.62 xx 10^-34 J s, e = 1.6 xx 10^-19C and m _e = 9.1 xx 10^-31 kg