A body weight $ W $ newton at the surface of the earth. Its weight at a height equal to half the radius of the earth will be

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

If both the mass and the radius of the earth decrease by $1\%$, the value of the acceleration due to gravity will

Gravitational acceleration on the surface of a planet is $\frac{\sqrt 6}{11}g$ , where $g$ is the gravitational acceleration on the surface of the earth. The average mass  density of the planet is $\frac{2}{3}\, times$ that of the earth. If the escape speed on the surface of the earth is taken to be $11\, kms^{-1}$, the escape speed on the surface of  the  planet in $kms^{-1}$ will be

Assuming the earth to be a sphere of uniform mass density, how much would a body weigh (in $N$) half way down to the centre of the earth if it weighed $250\; N$ on the surface?

Two planets have the same average density but their radii are ${R_1}$ and ${R_2}$. If acceleration due to gravity on these planets be ${g_1}$ and ${g_2}$ respectively, then