If mass of earth decreases by $25 \%$ and its radius increases by $50 \%$, then acceleration due to gravity at its surface decreases by nearly ……… $\%$

At  ….. $km$ height from the surface of earth the gravitation potential and the value of $g$ are  $-5.4 \times 10^7\, J kg^{-1}$ and $6.0\,m s^{-2}$ respectively . Take the radius of earth as $6400\, km$.

If a planet consists of a satellite whose mass and radius were both half that of the earth, the acceleration due to gravity at its surface would be ……… $m/{\sec ^2}$ ($ g$ on earth $= 9.8\, m/sec^2$ )

Given below are two statements :

Statement$-I:$ Acceleration due to gravity is different at different places on the surface of earth.

Statement$-II:$ Acceleration due to gravity increases as we go down below the earth's surface.

In the light of the above statements, choose the correct answer from the options given below

If the radius of the earth be increased by a factor of $5,$ by what factor its density be changed to keep the value of $g$ the same ?