Chapter 11, Problem 1OQ

To determine

The earth’s gravitational field when the atmospheric pressure is zero and the outer space would start at the planet’s surface.

Answer to Problem 1OQ

Option (b) Yes, and it would be essentially the same as the current value.

Explanation of Solution

The air particles are attracted towards the earth’s atmosphere due to the gravitational acceleration and every particles possess some mass (significantly small), so that it exerts force on the surface of earth. As the force acts on a unit area, the result will be the atmospheric pressure acts on the earth’s surface. As the gravity is suddenly switched off, that will lead to the evaporation of atmosphere and the value of atmospheric pressure becomes zero. And it will not affect the gravitational field of the planet.

Write the expression for the gravitational field, $g$.

    $g=\frac{Gm}{r^2}$        (I)

Here, $g$ is the gravitational field, $G$ is the gravitational constant, $m$ is the mass of the planet, $r$ is the radius of the planet.

The magnitude of the gravitational field depends on the mass and the radius of the planet.

Conclusion:

Since the magnitude of the planet’s gravitational field is not depend on the atmospheric pressure, option (b) is correct.

The mass as well as the radius of the planet remains same the magnitude of $g$ also remains same Thus, option (a) is incorrect.

Switching off the gravity would let the atmosphere evaporate away, but the switching off the atmosphere has no effect in the planet’s gravitational field Thus, option (c) is incorrect.

The atmosphere will evaporate away but the magnitude of the gravitational field of the planet remains same Thus, option (d) is incorrect.

Switching off the gravity will led to the evaporation of the atmosphere and the atmospheric pressure is not depending on the magnitude of the field Thus, option (e) is incorrect.