Question

variation of 'g' with altitude and depth.

Answer 1

The "universal law of gravity" is F = − ( G m M ) / r 2 F=−(GmM)/r2 where G is the "universal gravitational constant" (NOT "g") , m and M are the masses of the two attracting bodies and r is the distance between the centers of the two bodies. In particular, if we take M to be the mass of the earth and R to be the radius of the earth, F= -(GM/R^2)m= -gm so that g= GM/R^2. If r= R+ h, then we have F= -GmM/(R+ h)^2. We can, using the "generalized binomial formula", write ( R + h ) − 2 = R − 2 − 2 R − 3 h + (R+h)−2=R−2−2R−3h+ higher order terms in h so if h is small compared to R, we can approximate − G m M / ( R + h ) 2 −GmM/(R+h)2 by [itex]-GmM(R^{-2}- 2R^{-3}h= -GmM/R^2+ 2[GmM/R^{-2}](h/R)= -g(1- 2h/R). And, of course, both of the formulas have g(1 minus something) so as that "something" increases, g decreases.

I hope this will help you.

Answer 2

Hey mate. .


your ans..
may help you❤✌