Bonanza K35 pilot reported landing safely on the remaining runway when the engine lost power shortly after takeoff due to selection of a dry fuel tank that was reading 1/4 full.

Narrative

Today on Day 0 I was at ZZZ in a K35 bonanza. It was Vmc conditions.i had flown in for a personal lunch with a friend. I had left ZZZ1 airport with half tanks on both mains and drained the remaining fuel in both tip tanks; which I figured to be around 2-3 gals per side in the tips. I used fuel out of the right tank on the flight up which was about 5-7min flight. After lunch I decided to take my buddy up for a flight in the bonanza. The fuel indicated a little over half in the left side and between 1/4 to 1/2 in the right. I asked the airport staff where the self serve was and they told me there is no self serve at the airport. So I decided we would fly back to ZZZ1 to get fuel since it was so close. Before take off I noted that the fuel selector was on the right tank at 1/4-1/2 capacity and the left over 1/2. I decided to keep the fuel on the right tank to avoid switching just before take off and switch tanks in the air. The take off roll was normal and after lift off I retracted the gear at a positive rate. Seconds after I noted the gear was retracted I felt the physical and audible indication of the engine losing power. Altitude was 75-100ft agl. I immediately put the nose down and determined that my altitude and airspeed would not allow for troubleshooting of the engine. I put the gear down and was able to safely land and come to a stop on the remaining runway. I coasted onto a taxiway where we exited the plane and visually inspected it. No damage was done to the plane; persons on board; or any airport property. I got in the plane shortly after and switched to the left tank. The engine started and we taxied back to the fbo. After shutting the engine down at the fbo I visually saw little to no fuel in the fuel bladder; and a dry fuel bladder. The fuel indicator for the right tank still showed 1/4 capacity of gas. I filled the plane up; completed an engine run-up and departed back to ZZZ1. I'm very comfortable in the bonanza aircraft and decided to trust the fuel gauge. I failed to consider the yellow range of the fuel gauge and performed somewhat of a turning type takeoff which is prohibited by placard. This was a failure of my judgment. As a pilot I will learn from this and use it to better myself in the future and hopefully make aviation safer for everyone.