What is the long thing that sticks out between the Su-35's jet exhaust nozzles and what does it do?
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Image from airplane-pictures.net
Incidentally, the aircraft serial number is 901, while the one in your image has a number 902.
If you are speaking of the grey volume, according to this cutaway by Alexey Mikheyev, it contains a Radar Warning Receiver/Electronic Intelligence System. Basically a system designed to detect if an hostile weapon system is locking/has locked on you.