The value of acceleration due to gravity at Earth’s surface is $9.8\, m\,s^{-2}$. The altitude above its surface at which the acceleration due to gravity decreases to $4.9\, m\,s^{-2}$, is close to: (Radius of earth $= 6.4\times10^6\, m$)

Which of the following symptoms is likely to afflict an astronaut in space $(a)$ swollen feet, $(b)$ swollen face, $(c)$ headache, $(d)$ orientational problem.

If density of a planet is double that of the earth and the radius $1.5$ times that of the earth, the acceleration due to gravity on the surface of the planet 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

Assume there are two identical simple pendulum Clocks$-1$ is placed on the earth and Clock$-2$ is placed on a space station located at a height $h$ above the earth surface. Clock$-1$ and Clock$-2$ operate at time periods $4\,s$ and $6\,s$ respectively. Then the value of $h$ is $….km$ (consider radius of earth $R _{ E }=6400\,km$ and $g$ on earth $10\,m / s ^{2}$ )