The magnitude of the gravitational force exerted by the sphere and spherical shell is 9.68 * 10^-8 N.
Step-by-step explanation:
From the given information distance a= 1.49 m,
The particle of mass m1 = 7 kg to the center of the sphere (whose mass is m2 = 142 kg)
The radius R= 1.01 m of the sphere.
Thus, the gravitational force F exerted on a particle located at center from sphere increases linearly with the distance from the particle to the center of the sphere F = (G* m1 * m2 * a)/(R)^2
where G = 6.67*(10^-11) N * m^2 / kg^2,
F = (6.67*(10^-11) * 7 * 142 * 1.49) / (1.01)^2.
F = 9.68 * 10^-8 N.