A 100 kg ball of lead rests next to a 10 kg rock. Which statement below is true?
a. the lead ball and the rock have equal amounts of inertia
b. if the lead ball and the rock fell from the same height in a vacuum, the rock would hit the ground first because it is less massive.
c. on the moon both would have the samemass as on earth, but not the same weights as on earth.
d. because the lead ball has a larger mass than the rock, it will definitely have a larger volume than the rock
The correct statement is c. On the moon, both the lead ball and the rock would have the same mass as on Earth, but not the same weight as on Earth.
To determine which statement is true, let's analyze each option:
a. The lead ball and the rock have equal amounts of inertia.
Inertia is a property of matter that determines its resistance to change in motion. It is proportional to an object's mass. Given that the lead ball has a mass of 100 kg and the rock has a mass of 10 kg, we can conclude that the lead ball has a greater amount of inertia. Therefore, statement a is false.
b. If the lead ball and the rock fell from the same height in a vacuum, the rock would hit the ground first because it is less massive.
This statement is incorrect. When objects fall in a vacuum, neglecting air resistance, the mass of an object does not affect its acceleration due to gravity. Both the lead ball and the rock would experience the same acceleration and hit the ground at the same time. Therefore, statement b is false.
c. On the moon, both would have the same mass as on Earth, but not the same weight as on Earth.
This statement is true. The mass of an object remains constant regardless of the location in the universe. On the moon, both the lead ball and the rock would have the same mass as they do on Earth. However, the weight of an object depends on the gravitational pull exerted on it. Since the moon has a weaker gravitational force than Earth, both objects would weigh less on the moon compared to Earth. Therefore, statement c is true.
d. Because the lead ball has a larger mass than the rock, it will definitely have a larger volume than the rock.
The relationship between mass and volume is not determined solely by the mass of an object. Mass is a measure of the amount of matter in an object, while volume is a measure of the space occupied by an object. These two properties are not directly related. Therefore, statement d is false.
In conclusion, the correct statement is c. On the moon, both the lead ball and the rock would have the same mass as on Earth, but their weights would be different.