First, make sure you are using the correct headphones. The Samsung Galaxy R uses a 3.5 mm headphone jack. Check to see if the headphones you are using comply with these measurements.
If your headphone jack fits correctly and still does not produce sound, try a another set of headphones before considering replacing the headphone jack.
If you come to the conclusion that the headphone jack is faulty, replace the headphone jack.This guide will teach you how to remove the headphone jack: [guide|31648]
You can purchase a new headphone jack from SamsungParts.com, amazon.com, or ebay.