A solid sphere of uniform density has a mass of 6.6 × 104 kg and a radius of 0.51 m. What is
the magnitude of the gravitational force due to the sphere on a particle of mass 6.2 kg located at a
distance of (a) 1.5 m and (b) 0.096 m from the center of the sphere? (c) Write a general
expression for the magnitude of the gravitational force on the particle at a distance r ? 0.51 m
from the center of the sphere.
a) 1.2e-5
b) ?
c) | F on m | = K*r, where K = ?
Solution
(a)
F = GMm/r 2
= 6.673*10 -11
*6.6*10 4
*6.2/1.5 2
= 1.2136*10 -5
N
(b)
M inside = M*r inside
3
/R 3
= 6.6*10 4
*0.096 3
/ 0.51 3
M inside = 440.2 kg
F = GM inside m/r 2
= 6.673*10 -11
*440.2*6.2/0.096 2
= 1.98*10 -5
N
(c)
F = GM inside m/r 2
= G* M*r inside
3
/R 3
*m/r 2
F = GM/R 3
*r inside
where , K = GM/R 3
= 6.673*10 -11
*6.6*10 4
/ 0.51 3
K = 3.32*10 -5