$25$ A solid sphere has a uniformly distributed mass of $1\mathrm{.}0$ x $104$ kg and a radius of $1\mathrm{.}0$ m$.$ What is the magnitude of the gravitational force due to the sphere on a particle of mass m when the particle is located at a distance of $($a$)1\mathrm{.}5$ m and $($b$)0\mathrm{.}50$ 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 $1\mathrm{.}0$ m from the center of the sphere.