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

A satellite can be in a geostationary orbit around a planet at a distance $r$ from the centre of the planet. If the angular velocity of the planet about its axis doubles, a satellite can now be in a geostationary orbit around the planet if its distance from the centre of the planet is

A geo-stationary satellite is orbiting the earth at a height of $6 R$ above the surface of earth, $R$ being the radius of earth. The time period of another satellite at a height of $2.5 R$ from the surface of earth 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 potential energy of a satellite of mass $m$ and revolving at a height $R_e$ above the surface of earth where $R_e =$ radius of earth, is 

According to Kepler’s law the time period of a satellite varies with its radius as