I think this is a poor question because there is no indication about the material the ball is made of.  The assumption is that the ball must be rigid and hence immovable in its current condition, and that “metal” must be a better conductor of heat than the ball.  Now, suppose the ball is made of mercury and the metal is iron, and the current temperature is -50 degrees Celsius.  If you heat the metal base, the heat will be transferred to the ball, which will probably melt before the base!

Bad question.

The question could be looking for the key words: ” the holder expands MORE than the ball, hence the ball can be removed”. Your child’s answer only states the holder will expand, noting in fact both holder & ball will expand, though at different extent.

that’s kinda stupid isn’t it? considering it was specified that the metal holder was heated directly, why would we be expected to explain heat gain in comparison as if heat was applied equally to both? 

(b) Metal is a good conductor of heat. When the metal holder is immersed in the hot water, the metal holder will gain heat faster than the ball and expand more than the ball. Hence, the metal holder will become bigger than the ball and they can be separated.