26 (i) Give the expressions for the gravitational force exerted by the earth on a point mass m - Physics - Gravitation

Question

26 (i) Give the expressions for the gravitational force exerted by
the earth on a point mass m located above, below and on the surface
of earth Hence, deduce the expression for g on earth's surface
(ii) Two uniform solid spheres of radii R and 2R are at rest with
their spheres touching Determine the gravitational force of
attraction between them, if the density of spheres be p

OR
i) Deduce an expression for the obital velocity of a satellite in
the orbit Reduce into an orbit close to the surface of the earth
How is it related to escape velocity?
ii) Determine the gravitational pull between a sphere of mass M and
a uniform rod of length L and mass m as shown in the figure given
below:-

Vijay Shankar Yadav · Accepted Answer

Dear Student,
1) for above the surface Fa=mg'=GMem(Re+h)2        (Fa→ force above the surface )g'=gRe2(Re+h)2=g(1+hRe)-2=g(1-2hRe) (by boinomial expansion) for below the surface Fb=mg''=GMm(Re-h)2      (Fb→ force below the surface )g''=GMe(Re-h)3Re2=g(1-hRe)2)We have newtons force law acts for point mass so for apply this we have to make them as a point mass which can be if we assuming all the mass is acting ont he center of thr bodyhence  force =G×43π(2R)3ρ×43π(R)3ρ(3R)2=128Gρ2π2R481
kindly post different question in defferent threads
Regards