Let’s look at some gravitational potentials and the density profiles that can generate them. i) for rho(r) = rho◦r 2 ◦/r2 , what is the corresponding gravitational potential? ii) for φ(r, z) = φ◦ ln[ r 2 ◦+r 2+z 2/q2 r2 ◦ ], what is the corresponding density profile rho(r, z)? in this expression, the constant q controls the axis ratio of the potential, where q = 1 would be spherically symmetric and q < 1 means that the potential is "flattened" a bit along the z-axis. does something strange happen at large distances along the z axis if q < 0.7 ?

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.