Final answer:
The statement is false because gravity on the moon is weaker than on Earth, but since a balance scale measures mass and mass is constant, the balance would remain level on the moon.
Step-by-step explanation:
The statement is false. When a 1-kg iron weight and a book are placed on opposite sides of a balance scale on Earth and it balances, this indicates that the book also has a mass of 1 kg, as the scale is comparing mass, not weight. If these objects are taken to the moon and the same balance experiment is performed, the scale would still be level. This is because gravity does not affect the balance of mass; a balance scale measures mass, which is constant everywhere.
However, while it's true that gravity is weaker on the moon, the assertion that gravity is uniform on the moon as it is on Earth is incorrect. Gravity is uniform on the moon's surface regarding the moon's gravity, but it is about 1/6th as strong as Earth's gravity. Nevertheless, since a balance scale measures mass, which does not change with location, the balance would remain level on the moon.