In a satellite if the time of revolution is $T$, then $P E$ is proportional to ..........
$T^{1 / 3}$
$T^3$
$T^{-2 / 3}$
$T^{-4 / 3}$
A particle of mass $M$ is placed at the centre of a uniform spherical shell of mass $2M$ and radius $R$. The gravitational potential on the surface of the shell 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
The magnitudes of gravitational field at distances $r_1$ and $r_2$ from the centre of a uniform sphere of radius $R$ and mass $M$ are $F_1$ and $F_2$ respectively. Then-
In order to make the effective acceleration due to gravity equal to zero at the equator, the angular velocity of rotation of the earth about its axis should be $(g = 10\,m{s^{ - 2}}$ and radius of earth is $6400 \,kms)$
A particle of mass $m$ is placed at the centre of a uniform spherical shell of mass $3\,m$ and radius $R$. The gravitational potential on the surface of the shell is