Question

What if somebody threw a ball through the north pole to the south pole and no core present. so no melting

Answer 1

Dude. Your imagination cannot be guaranteed because you can't throw a ball from the north pole to south pole even if you dig out a tunnel connecting the poles. as you know that gravity of every body is zero at it's centre and the ball surely stops at the centre. If there was or wasn't a core but the same happens...