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How to derive variation of "g" with depth in easy type |
| Answer» let us consider an object is placed at a point having mass m below the surface of the earthat the surface of earth g=GM/R^2 let at point a acceleration due to gravity be g g=GM/R^2. ..........eq.1let mass M=p(density)×V(volume) M=p×4/3πR^3put the value of M in eq. 1 g=Gp×4/3πR^3/R^2 g=Gp×4/3πR. ........eq.2let at point b the value of g is g\' g\'=GM/(R-x)^2. .......eq.3let mass M= p×V M=p×4/3π(R-x)^3. put the value of M in eq. 3 g\'=Gp×4/3(R-x)^3/(R-x)^2 g\'=Gp×4/3(R-x) .........eq.4divide eq.4 by eq.2 g\'/g=Gp×4/3π(R-x)/Gp×4/3πR g\'/g=R-x/R g\'/g=(1-x/R) g\'=g(1-x/R) | |