A body of mass $m$ is situated at distance $4R_e$ above the Earth's surface, where $R_e$ is the radius of Earth how much minimum energy be given to the body so that it may escape
$mgR_e$
$2\,mgR_e$
$\frac {mgR_e}{5}$
$\frac {mgR_e}{16}$
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
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.
The dependence of acceleration due to gravity $g$ on the distance $r$ from the centre of the earth assumed to be a sphere of radius $R$ of uniform density is as shown figure below
The correct figure is
Which of the following statements are true about acceleration due to gravity?
$(a)\,\,'g'$ decreases in moving away from the centre if $r > R$
$(b)\,\,'g'$ decreases in moving away from the centre if $r < R$
$(c)\,\,'g'$ is zero at the centre of earth
$(d)\,\,'g'$ decreases if earth stops rotating on its axis
Two identical spheres are placed in contact with each other. The force of gravitation between the spheres will be proportional to ($R =$ radius of each sphere)