Using (-GM/r^2)(r hat) I\'m having a lot of trouble understanding this can you w

Question

Using (-GM/r^2)(r hat) I'm having a lot of trouble understanding this can you walk me through this step by step Problem 1: A mass m is located a distance a from the origin along the y- axis as see in the diagram at right. a) What is the gravitational field at the location given by the coordinate x 0, y 2a? b) What is the gravitational field at the location given by the coordinate x =-a, y -2a? If you were to place a mass Mat the location given in part (b), what is the force it experiences due to m? c)

Explanation / Answer

a) Let 'p' (0,2a) is the pt at which the field to be found. r = (2a-a) j = a j ; g = (Gm/a^2) j

b) now P( -a,-2a) therefore r = ( -a)i + (-2a-a)j = (-ai-3aj) ; r = sqrt(10) a ; r (hat) = -(i+3j)/ sqrt(10)

g = -{ Gm ( i+3j)} / ( 10^3/2 * a^2)

c) F = -GMm(i+3j)}/(10^3/2*a^2)

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