d
We known that \(\overrightarrow {{\tau _c}}  = \frac{{\overrightarrow {d{L_c}} }}{{dt}}\)

Where \(\overrightarrow {{\tau _c}} \) torque about the center of mass of the body and \(\overrightarrow {{L_c}} \) \(=\) Angula momentum about the center of mass of the body. central forces act along the center of mass. Therefore torque about center of mass is zero.

When \(\overrightarrow {{\tau _c}} \) \(= 0\)    then \(\overrightarrow {{L_c}} \) \(=\) constt.