The centripetal force required to keep an object in circular motion increases if the mass of the object doubles. This is because the centripetal force required to keep an object in circular motion is directly proportional to the mass of the object. The formula for centripetal force is Fc = mv²/r, where Fc is the centripetal force, m is the mass of the object, v is the speed of the object, and r is the radius of the circular path. As you can see from the formula, the centripetal force is directly proportional to the mass of the object (m). So, if the mass of the object doubles, the centripetal force required to keep it in circular motion will also double.