Weakly Interacting Massive Particles (WIMPs) are one of the possible candidates for Dark Matter in the Universe. In this problem, we study the possibility for a WIMP to be captured by a neutron starl. 1. The laws of non-relativistic mechanics predict an acceleration F= = of the WIMP at a distance r from the centre of a neutron star of mass M = 3 x 10* kg and radius R = 10 km. The gravitational constant is G ~ 6.67 x 10-! N.m/kg2. Calculate the acceleration of a WIMP at the surface of the neutron star. Assuming that it is initially at rest, how much time would it take for a WIMP with this acceleration to reach 10% of speed of light? Conclude on the validity of the above equation of motion