Common Sense was written as a means to encourage American independence. When Paine asks rhetorical questions, he is not really asking questions that have no answers. He is trying to inspire his listeners/readers to answer these questions for themselves. In the third section, Paine states that any future connection to Britain will be "forced and unnatural" and eventually "more wretched than the first." He then asks a series of rhetorical questions:
But if you say, you can still pass the violations over, then I ask, hath your house been burnt? Hath your property been destroyed before your face? Are your wife and children destitute of a bed to lie on, or bread to live on? Have you lost a parent or a child by their hands, and yourself the ruined and wretched survivor? If you are not, then are you not a judge of those who have.
Paine appeals to those who have been oppressed by the British government. He asks if they have been wronged in ways such as these. He means to stir up their anger and their desire to be free of this tradition of oppression. He also appeals to those who have not been wronged (perhaps the rich and those still loyal to the British crown). He adds that if they have not been oppressed the way others have, then they have no right to judge them and their desire for independence.
Paine is being a bit Socratic in asking questions, in getting the readers to answer for themselves. This strategy allows the readers to question themselves and have the independence, individually and as a group, to form their own answers, which Paine hopes will be a call for revolution.