On the surface of the moon, where the acceleration due to gravity is about one-sixth that of Earth, a 100-kg astronaut would have a mass of_____ and a weight of _____

A. 100kg, 1000N
B. 16.6kg, 166N
C. 100kg, 166N
D. 600kg, 1000N

C. 100kg, 166N

Mass remains constant but weight would be changed because of the gravity.

The equation for force is
F=ma
F=100*1.66
F=166N

To determine the mass and weight of the astronaut on the surface of the moon, we need to understand the terms "mass" and "weight."

The mass of an object is a measure of the amount of matter it contains and is typically measured in kilograms (kg). Mass remains the same regardless of the gravitational field.

Weight, on the other hand, refers to the force exerted on an object due to gravity. It is calculated by multiplying the mass of an object by the acceleration due to gravity. Weight is measured in Newtons (N) and can vary depending on the strength of the gravitational field.

In this scenario, the acceleration due to gravity on the Moon is about one-sixth that of Earth. Therefore, to find the weight of the astronaut, we need to multiply their mass by one-sixth (1/6) of the acceleration due to gravity on Earth.

Let's apply this knowledge to the given options:

A. 100kg, 1000N: According to this option, the mass remains 100kg, which is correct. However, the weight of the astronaut on the Moon would be one-sixth (1/6) of the weight on Earth, so the weight should be less than 1000N. Therefore, this option is incorrect.

B. 16.6kg, 166N: Here, the mass is decreased to one-sixth (1/6) of 100kg, which equals 16.6kg. The weight is then calculated by multiplying the mass by one-sixth (1/6) of the acceleration due to gravity on Earth, resulting in 166N. Therefore, this option is correct.

C. 100kg, 166N: This option has the correct mass of 100kg, but the weight given is the same as the previous option. The weight needs to be one-sixth (1/6) of Earth's weight, so 166N would be incorrect. Therefore, this option is incorrect.

D. 600kg, 1000N: In this option, both the mass and weight are incorrect. The mass should remain 100kg, as it does not change regardless of the gravitational field. The weight should be less than 1000N since the lunar gravity is only one-sixth that of Earth. Therefore, this option is incorrect.

Based on the explanations above, the correct answer is B. 16.6kg, 166N.