I am using containers which are well drained. Watering daily . Any comments are welcome

What did you fill the containers with?
Also how big -- deep and wide -- is the container?

Carrots have a massive taproot. If the container is not deep enough, the taproot won't have room to shoot down into the soil. How deep is your container?

Looks like a container problem, Container should be at least 12 inches deep.

Sorry for the late response. Well, my container is about 11 inch (not too bad I guess ). Probably I didn't make good thinning (about 2 inches apart. The one shown here was just close to the wall of the container). However, I feel that 2 inch spacing should yield carrots longer that this .. Am I correct?

One other possibility is Sun. My carrots get direct sun light for about 4 hours a day at maximum (the weather here is warm, and clouds are very rare. Average temperature is 65-80, and the direct sun is hot).

Carrots really need six to eight hours of sun. They do decent in partial shade, but for a good yield you need six to eight.

The container seems fine. 2-3 inches is far enough for carrots (I've grown them closer.) And, yes, with optimal conditions 2 inches should yield much longer carrots.

How often are you watering them? They need ~1 inch per week.

Yes @Agonistes
I got longer carrots later on, particularly those that were better spaced, and looked healthy and non-splitted. it made me feel happy, and it tasted really sweet. Have a look at the picture. I hope I'll get longer ones next time.
Thanx