At what distance above and below the surface of the earth a body will have same weight, (take radius of earth as $R$.)

If the mass of earth is $80$ times of that of a planet and diameter is double that of planet and $‘g’$ on earth is $9.8\,m/{s^2}$, then the value of $‘g’ $ on that planet is ........ $m/{s^2}$

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

If the change in the value of $‘g’$ at a height $h$ above the surface of the earth is the same as at a depth $x$ below it, then (both $x$ and $h$ being much smaller than the radius of the earth)

The value of g on the earth's surface is $980\,cm/{\sec ^2}$. Its value at a height of $64 \,km$ from the earth's surface is ........ $cm/{\sec ^2}$

(Radius of the earth $R = 6400$ kilometers) 

The mass density of a spherical body is given by $\rho \left( r \right) = \frac{k}{r}$ for $r \leq R\,\,$ and $\rho \left( r \right) = 0\,$ for $r > R$ , where $r$ is the distance from the centre. The correct graph that describes qualitatively the acceleration, $a$, of a test particle as a function of $r$ is