To overcome the effect of weightlessness in an artificial satellite

The correct option is: The compartment of astronaut is kept on the periphery of rotating wheel like satellite

Underlying Physics:
In an orbiting artificial satellite, both the satellite and the astronauts inside are in a state of continuous free fall towards the Earth. Because they are accelerating at the same rate under gravity, there is no contact force (normal reaction) between the astronaut and the satellite's floor, resulting in the sensation of weightlessness.

To overcome this effect, we can generate artificial gravity by rotating the satellite. When a satellite is shaped like a wheel and rotated about its central axis, any object inside experiences a centrifugal force directed radially outward from the axis of rotation. This force can simulate gravity.

The simulated gravitational acceleration is given by the formula:

$a={\omega }^{2}R$
where:
- $a$ is the simulated acceleration,
- $\omega$ is the angular velocity of the rotating satellite, and
- $R$ is the distance from the axis of rotation.

From the equation, we can see that if the compartment is at the center of the satellite (where $R=0$), the simulated acceleration is zero. To achieve a significant artificial gravity effect, $R$ must be as large as possible. Therefore, the astronaut's compartment must be kept on the periphery (outer boundary) of the rotating wheel-like satellite, allowing them to experience a normal force pushing back against them, mimicking gravity on Earth.