Why did france's entry into war with austria in 1792 have an immediate radicalizing effect on the revolution?

The correct answer is C. When the French armies proved dreadfully unprepared for battle, the authority of the Assembly was challenged, and angry crowds instigated more radical political change.

They didn't want to fight a war that they would lose and losing would mean that times would be even harder than they were at the time, and times were hard indeed. They decided to take the matter into their own hands and change the ruler in order to prevent misery and bloodshed.