Question

An astronaut in a space station orbits above the Earth. In the space station, the acceleration due to gravity is 7.5m/s2. On Earth, the acceleration due to gravity is 10m/s2. Which statement about the astronaut’s mass and weight in the space station is correct?
A. Mass of astronaut - same as on the earth, weight of astronaut - less than on the earth
B. Mass of astronaut - same as on the earth, weight of astronaut - greater than on the earth
C. Mass of astronaut - lower than as on the earth, weight of astronaut - less than on the earth
D. Mass of astronaut - lower than as on the earth, weight of astronaut - greater than on the earth

Answer 1

We must understand what mass and weight are. The mass is defined as the amount of matter contained inside a body.

Complete step by step answer:
Astronaut is present inside a space station which is orbiting around the earth with some centripetal acceleration. The centripetal acceleration of the space station is balanced by the acceleration due to gravity of the earth in such a way that the net acceleration inside the space station is 7.5m/s2. We are also given that the acceleration due to gravity of the earth is 10m/s2, and so we must comment on the mass and weight of the astronaut inside the space station compared to that on earth.
Firstly, we must understand what mass and weight are. The mass is defined as the amount of matter contained inside a body. It is an inbuilt property of her body and does not depend on any external factor (in non-relativistic conditions).
The weight is defined as the force with which a body is being pulled towards a planet. It depends upon the gravitational attraction of the planet, the stronger the pull is the greater will be the mass (depends on acceleration due to gravity of the planet).
Since now we know that only the weight of the astronaut will depend on acceleration due to gravity, therefore we can see that, the weight of the astronaut will be greater on earth than on the space station, because of the difference in the acceleration due to gravity. The mass of the astronaut will be the same in both places.

So, the correct answer is “Option A”.

Note:
Here we are assuming that all of this is in non-relativistic conditions. In relativistic conditions (at speeds close to the speed of light), the mass of the astronaut will not remain constant and might differ.