The radii of two planets are respectively ${R_1}$ and ${R_2}$ and their densities are respectively ${\rho _1}$ and ${\rho _2}$. The ratio of the accelerations due to gravity at their surfaces is

The international space station is maintained in a nearly circular orbit with a mean altitude of $330 \,km$ and a maximum of $410 \,km$. An astronaut is floating in the space station's cabin. The acceleration of astronaut as measured from the earth is

Given below are two statements:

Statement $I:$ Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface.

Statement $II:$ Acceleration due to earth's gravity is same at a height ' $h$ ' and depth ' $d$ ' from earth's surface, if $h = d$.

In the light of above statements, choose the most appropriate answer form the options given below

If the mass of the Sun were ten times smaller  and the universal gravitational constant were ten times larger in magnitude, which of the following is not correct? 

Find the magnitude of acceleration due to gravity at height of $10\, km$ from the surface of earth.