The acceleration due to gravity on the Moon is only about 1/6 of that on Earth. An astronaut whose weight on Earth is 600 N travels to the lunar surface. His mass as measured on the Moon is
A) 600 kg.
B) 100 kg.
C) 61.2 kg.
D) 10.0 kg.
E) 360 kg.

Question

Quizplus · Accepted Answer

The weight of the astronaut on the moon can be found using the formula:

Weight = mass x acceleration due to gravity

On the moon, the acceleration due to gravity is 1/6 of that on Earth, so:

Weight on moon = (mass of astronaut) x (1/6 x acceleration due to gravity on Earth)
Weight on moon = (mass of astronaut) x (1/6 x 9.81 m/s²)
Weight on moon = (mass of astronaut) x 1.635 m/s²

We know that the weight of the astronaut on Earth is 600 N, so:

Weight on Earth = (mass of astronaut) x (acceleration due to gravity on Earth)
600 N = (mass of astronaut) x 9.81 m/s²

Solving for the mass of the astronaut on Earth:

mass of astronaut on Earth = 600 N ÷ 9.81 m/s²
mass of astronaut on Earth = 61.17 kg

Now we can use this mass to find the mass of the astronaut on the moon:

Weight on moon = (mass of astronaut on moon) x 1.635 m/s²
Weight on moon = 600 N

Substituting mass of astronaut on moon:

(mass of astronaut on moon) x 1.635 m/s² = 600 N

mass of astronaut on moon = 600 N ÷ 1.635 m/s²
mass of astronaut on moon = 367.35 kg

Therefore, the mass of the astronaut on the moon is approximately 61.2 kg (to one decimal place). Answer choice C is correct.

The Acceleration Due to Gravity on the Moon Is Only