How does a mobile phone vibrate without any external force? By Newton's law, any body can't move without any external force
That's not true, Newtons's laws do not say that. What's important here is conservation of momentum. Inside the phone, there is an oscillating mass. While the mass inside has a momentum and thus a velocity in one direction, the (friction-free) phone has to have the same momentum in the opposite direction. It "vibrates".
Homework: Get on a skateboard (best kneeling, not standing), take a decent mass with you (e.g. a cobblestone) and move it forth and back in front of your chest. Now, put a large cardboard box over your head (e.g. from a refrigerator) and you have a box that moves back and forth without any external force.
If you want translation instead of oscillation, you have to divide the object, making one part go in one direction and the other in the opposite direction (again, with the same momentum). That's how rockets work, by expelling the reaction products of their fuel at high speed in the opposite direction. Again, without "external" force.
Alternatively, you can just sit in a chair, and punch the air really fast. When your arm moves out, your body moves back, when your arm moves back in, your body moves toward the arm.
I've taken a phone apart to confirm the "imbalanced weight" coming off the shaft of a miniature motor. Which essentially creates a moment arm off-center of the shaft, once the motor begins to turn, this torque (force X distance) lets momentum (mass X velocity) move energy through the body of the motor, to the base of the motor, through the phone, and further dissipated through your body. Hence, felt vibration through your pocket.
It keeps its center of gravity constant. But since there is a rotating eccentric weight inside the body center moves in opposite fashion from the rotating weight making the phone appear to vibrate.
This is similar to recoil from a gun, or if you are on skates and try to spin a weight in the end of a rope it will make you skate back and forth. It would be fun to watch though!
Wow...I have read the answers of some 5 years ago and feeling surprised that nobody knows physics here!
Newton says: sum of internal forces is always zero PROVIDED THAT there is no chemical/biological conversion(of energy). That means the energy of the system shall remain same also.
In case of a vibrating phone, the stored electrical energy converts into kinetic energy and causes a phone to vibrate. Ofcourse, after vibrating the energy stored decreases.
Similarly, a car moves by converting the stored chemical energy of the fuel into heat and then into mechanical energy.
Without any external force, the work is done by wasting internal energy(not wasting, but converting energy into other form)
Hope it helps.