Acceleration due to gravity on moon is $\frac 16$ of the acceleration due to gravity on earth. If the ratio of densities of earth $({\rho _e})$ and moon $({\rho _m})$ is $\left( {\frac{{{\rho _e}}}{{{\rho _m}}}} \right) = \frac{5}{3}$ then radius of moon $R_m$ in terms of $R_e$ will be

The height of the point vertically above the earth’s surface, at which acceleration due to gravity becomes $1\%$ of its value at the surface is (Radius of the earth $= R$)

If both the mass and the radius of the earth decrease by $1\%$, the value of the acceleration due to gravity will

The approximate height from the surface of earth at which the weight of the body becomes $\frac{1}{3}$ of its weight on the surface of earth is $..........km$ : [Radius of earth $R =6400 \,km$ and $\sqrt{3}=1.732]$

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

The weight of a body on the surface of the earth is $100\,N$. The gravitational force on it when taken at a height, from the surface of earth, equal to onefourth the radius of the earth is $..........\,N$