a The pressure force per unit area at the center of a star i

(a) The pressure (force per unit area) at the center of a star is high because it has to support the star against gravitational contraction. Using only dimensional analysis, derive an expression for the required pressure. Hint: There will be a G in your answer.

Solution

the pressure at the centre of star due to gravity must be equal to the pressure created due to nuclear reactions , the pressure P can be estimated from pascal\'s principle   

                                                         Pressure P = gR ; is star density =mass/volume, = M / 4piR^3 / 3

                               g is star gravitational acceleration =g=(G*M)/(R^2)

                                                                                   and R is the radius of the star

                                              P = 3 *pi * G * M^2 / 4 * R^4