Two planets move around the sun. The periodic times and the mean radii of the orbits are ${T_1},\,{T_2}$ and ${r_1},\,{r_2}$ respectively. The ratio ${T_1}/{T_2}$ is equal to
${({r_1}/{r_2})^{1/2}}$
${r_1}/{r_2}$
${({r_1}/{r_2})^2}$
${({r_1}/{r_2})^{3/2}}$
The Earth is assumed to be a sphere of radius $R$. A platform is arranged at a height $R$ from the surface of the Earth. The escape velocity of a body from this platform is $fv$, where $v$ is its escape velocity from the surface of the Earth. the value of $f$ is
A spherical part of radius $R/2$ is excavated from the asteroid of mass $M$ as shown in the figure. The gravitational acceleration at a point on the surface of the asteroid just above the excavation is
The weight of a body on the surface of the earth is $63\, N$. What is the gravitational force on it due to the earth at a height equal to half the radius of the earth ? (in $N$)
Two spheres of masses $m$ and $M$ are situated in air and the gravitational force between them is $F$. The space around the masses is now filled with a liquid of specific gravity $3$. The gravitationalforce will now be
A body of mass $m$ is lifted up from the surface of the earth to a height three times the radius of the earth. The change in potential energy of the body is
where $g$ is acceleration due to gravity at the surface of earth.