If the radius of the Earth were to shrink by half while its density remains constant,what would be the weight of an object on the surface of the Earth?

Assertion $(A)$: $A$ particle of mass $m$ dropped into a hole made along the diameter of the Earth from one end to the other possesses simple harmonic motion.
Reason $(R)$: Gravitational force between any two particles is inversely proportional to the square of the distance between them.

$A$ tunnel is dug through the centre of the earth. Show that a body of mass $m$ when dropped from rest from one end of the tunnel will execute simple harmonic motion.

The weight of a body on the surface of the earth is $100\,N$. The gravitational force on it when taken at a height,from the surface of earth,equal to one-fourth the radius of the earth is $..........\,N$.

An object is taken to a height above the surface of the Earth at a distance of $\frac{5}{4} R$ from the center of the Earth,where the radius of the Earth is $R = 6400 \, km$. The percentage decrease in the weight of the object will be $....\%$.

The ratio of the height $h$ above the surface of the Earth to the depth $d$ below the surface of the Earth,for which the gravitational accelerations are the same (assuming small heights),is: