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 value of the acceleration due to gravity is $g _{1}$ at a height $h =\frac{ R }{2}( R =$ radius of the earth) from the surface of the earth. It is again equal to $g _{1}$ at a depth $d$ below the surface of the earth. The ratio $\left(\frac{ d }{ R }\right)$ equals

At  ..... $km$ height from the surface of earth the gravitation potential and the value of $g$ are  $-5.4 \times 10^7\, J kg^{-1}$ and $6.0\,m s^{-2}$ respectively . Take the radius of earth as $6400\, km$.

A clock $S$ is based on oscillation of a spring and a clock $ P$ is based on pendulum motion. Both clocks run at the same rate on earth. On a planet having the same density as earth but twice the radius

A newly discovered planet has a density eight times the density of the earth and a radius twice the radius of the earth. The time taken by $2\, kg$ mass to fall freely through a distance $S$ near the surface of the earth is $1$ second. Then the time taken for a $4\, kg$ mass to fall freely through the same distance $S$ near the surface of the new planet is ....... $\sec$.

Imagine a new planet having the same density as that of earth but it is $3$ times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is $g$ and that on the surface of the new planet is $g^{\prime}$, then