Answer
The object's velocity after it has fallen a distance of $0.01m$ is $3.27\times10^5m/s$
Work Step by Step
The mass of the neutron star $M_n=2\times10^{30}kg$ and its radius $r=5\times10^3m$
The gravitational constant $G=6.67\times10^{-11}Nm^2/kg^2$
The gravitational acceleration on this star can be calculated by $$a_g=G\frac{M_n}{r^2}=5.34\times10^{12}m/s^2$$
Now take a look at the object, which has initial velocity $v_0=0$ and the distance fallen $x=0.01m$
The object's velocity after it has fallen distance $x$ is $$v^2=v_0^2+2a_gx=2a_gx$$ $$v^2=1.07\times10^{11}m^2/s^2$$ $$v=3.27\times10^5m/s$$
