What's the diameter of the rod?
Really, unless you have sufficient area, if this thing takes any strain at all, gluing is probably not on --- or it would need to be a kind of glue that melts the surface of the plastic, thus effectively welding the pieces rather than sticking.
Here's my other, crazy and tricky idea. Drill into the broken pieces with a small drill and insert a piece of steel (pin? needle?) which will then support the joint. It should be a loose fit, allowing space for glue around the steel. I just have no idea how one would accurately line up the holes.
This sort of break is so frustrating: good luck!
Best glue? My favourite is called JB Weld. It is like a plastic-metal-cum-epoxy-glue. You can use it as a contact adhesive, and/or you can build it up around the join and then file/sand it. I find it much more reliable than Araldite, but... available in India? I think it is American, and I have trouble finding it in London!
<Crossposted with hitensitapara...>
Good idea, if feasible. Even a wood dowel?