JEE Main · 2007 · 29 Apr 2007 · Offline · Rotational Mechanics

A central force always points along the line joining the particle to the fixed centre, so it is parallel to the position vector $\vec{r}$. The torque about that centre, $\vec{\tau }=\vec{r}\times \vec{F}$, is then the cross product of two parallel vectors and vanishes. Since $\frac{d\vec{L}}{dt}=\vec{\tau }=0$, the angular momentum stays constant, and this constancy follows directly from the torque being zero.