If the radius of the Earth were to shrink by half,its mass remaining the same,what would be the weight of an object on its surface?

$A$ 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 a $2\, kg$ 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 ....... $\sec$.

What is the time period of a seconds pendulum on a planet whose mass and radius are twice that of the Earth?

If a man at the equator would weigh $(3/5)^{th}$ of his weight,the angular speed of the earth is

Find the gravitational field at a distance of $2000\, km$ from the center of the Earth. (in $m/s^2$)
(Given: $R_{\text{earth}} = 6400\, km$,$r = 2000\, km$,$M_{\text{earth}} = 6 \times 10^{24}\, kg$)

The acceleration due to gravity becomes $\left(\frac{g}{2}\right)$ ($g =$ acceleration due to gravity on the surface of the earth) at a height equal to