Two spherical planets $A$ and $B$ have the same mass,but their densities are in a ratio $8:1$. For these planets,the ratio of acceleration due to gravity at the surface of $A$ to its value at the surface of $B$ is:

Assuming the Earth to be a sphere of uniform mass density,the weight of a body at a depth $d = R/2$ from the surface of the Earth,if its weight on the surface of the Earth is $200 \, N$,will be $........... \, N$ (Given $R =$ Radius of Earth).

The value of $g$ on the Earth's surface is $980 \, cm/s^2$. Its value at a height of $64 \, km$ from the Earth's surface is ........ $cm/s^2$ (Radius of the Earth $R = 6400 \, km$).

The percentage decrease in the weight of a body when taken to a height of $48 \text{ km}$ above the surface of the earth is (Radius of the earth is $6400 \text{ km}$) (in $\%$)

$A$ spherical part of radius $R/2$ is excavated from an asteroid of mass $M$ and radius $R$ as shown in the figure. The gravitational acceleration at a point on the surface of the asteroid just above the excavation is

If the earth rotates faster than its present speed,the weight of an object will