If these puppies were just recently taken from their mother, then I would say it's missing Mom. Some dogs are more vocal than others about this. You might try giving them both a quick and gentle bath, and make sure their bedding is fresh and clean. The following explains why I say this:
When I went and picked up our little Shih Tzu, at only 8 wks old, it was about a 20 min. ride back to our house, and that little darling curled right up beside me in the car, never making a sound. When I got her home, I put her in the grass to pee, brought her in the house and she started playing immediately. A short time later I bathed her, (could no longer stand the 'doggie' smell of her Mom, and am now wondering if perhaps getting Mom's smell off her is why, but she never once cried for her mom. If there was ever another puppy to come into my life, I think I would bathe it immediately also.
At the same time, maybe this puppy is bothered by worms and hurting in some way. Have you had them both checked by a vet and had shots given them? This pup also could maybe use more food than the other pup and is whining because he's hungry. There are many things it could be, but it might be worth your while, if the pup is not acting sickly to do what I advised in the first part of my answer about the bath.
Good luck, and may you enjoy a long and healthy life with your new puppies.
