If the radius of the Earth becomes double while its mass remains unchanged,what will be the change in the weight of an object of mass $m$ on the surface of the Earth?

The acceleration due to gravity near the surface of a planet of radius $R$ and density $d$ is proportional to

$A$ body weighs $500 \,N$ on the surface of the earth. At what distance below the surface of the earth will it weigh $250 \,N$ (in $\,km$)? (Radius of earth, $R = 6400 \,km$)

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 towards the centre if $r < R$
$(c)$ '$g$' is zero at the centre of the Earth
$(d)$ '$g$' decreases if the Earth stops rotating on its axis

The linear speed of a particle at the equator of the earth due to its spin motion is $V$. The linear speed of the particle at latitude $30^{\circ}$ is:

If a planet has a mass and radius both half that of the Earth,the acceleration due to gravity at its surface would be ......... $m/s^2$ ($g$ on Earth $= 9.8\, m/s^2$)