If the density of the earth is doubled keeping its radius constant,then the acceleration due to gravity will be........ $m/s^2$. $(g = 9.8\,m/s^2)$

$A$ body weighs $700\,gm\,wt.$ on the surface of the earth. How much will it weigh on the surface of a planet whose mass is $\frac{1}{7}$ and radius is half of that of the earth?

An astronaut inside a small spaceship orbiting around the earth cannot detect gravity. If the space station orbiting around the earth has a large size,can he hope to detect gravity?

The acceleration of a body due to the attraction of the earth (radius $R$) at a distance $2R$ from the surface of the earth is ($g =$ acceleration due to gravity at the surface of the earth).

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.

The acceleration due to gravity on the moon is $\frac{1}{6}$ times the acceleration due to gravity on the earth. If the ratio of the density of the earth $\rho_e$ to the density of the moon $\rho_m$ is $\frac{5}{3}$,then the radius of the moon $R_m$ in terms of the radius of the earth $R_e$ is: