If a neutron star was in the solar system what would happen and how would it effect the planets?

If a neutron star just appeared in our solar system just in between mars and earth would it instantly be attracted to the earths surface. Because a neutron star can accelerate and force objects onto its surface at around I think 100,000 miles per hour. Something as soft as a marsh mellow if just instantly appeared on the surface of the neutron star would have more destructive power than a atomic bomb. So what would happen to the neutron star if it appeared in between the half way distance between earth and mars. Also if the neutron star crashed into earth or mars, because of the neutron stars strong gravity. Would it instantly attract objects like rocks and other things from earths surface onto itself with its strong gravity, or even rip a hole through the earths surface with its strong gravity making its mass larger. Because a neutron star can only get so large in mass and then it will collapse into a black hole. Would this happen to the neutron star on earth or mars, would the neutron star collapse into a black hole from its mass getting larger from attracting debree like rocks and then destroy any planet even Jupiter from turning into a black hole. So is it impossible for a neutron star to exist in our solar system, or would its gravitational pull not attract it to the planets as long as it was far away enough between them. Thank you for your help