Final answer:
The hose connections should be made in such a way that the solenoid current flows through the cylinder, causing it to extend when the solenoid sol-1a is energized. The cylinder gets hot when the cannon is fired due to the conversion of kinetic energy into thermal energy.
Step-by-step explanation:
When the solenoid sol-1a is energized, it creates a magnetic field. According to Faraday's law of electromagnetic induction, this changing magnetic field induces an electric current in the metal cylinder. This current creates a force that opposes the motion of the cylinder, as stated by Lenz's law.
The hose connections should be made in such a way that the solenoid current flows through the cylinder. This can be achieved by connecting one end of the solenoid coil to one end of the cylinder, and the other end of the solenoid coil to the other end of the cylinder. When the solenoid current is turned on rapidly, the induced current in the cylinder will cause a repulsive force, pushing the cylinder outwards, extending it.
The reason why the cylinder gets live/hot when the cannon is fired is due to the energy dissipation in the form of heat. As the cylinder is expelled rapidly from the solenoid coil, there is a sudden change in motion. This results in kinetic energy being converted into thermal energy, causing the cylinder to heat up.