The height at which the weight of a body  becomes ${\frac{1}{16}}^{th}$ , its weight on the surface of earth (radius $R$), is

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

The acceleration due to gravity at pole and equator can be related as

A body weighs $144 \,N$ at the surface of earth. When it is taken to a height of $h=3 \,R$, where $R$ is radius of earth, it would weigh .......... $N$

Two planets $A$ and $B$ of radii $R$ and $1.5 R$ have densities $\rho$ and $\rho / 2$ respectively. The ratio of acceleration due to gravity at the surface of $B$ to $A$ is :

Given below are two statements :

Statement $I$ : The law of gravitation holds good for any pair of bodies in the universe.

Statement $II$ : The weight of any person becomes zero when the person is at the centre of the earth. In the light of the above statements, choose the correct answer from the options given below.