The depth at which the effective value of acceleration due to gravity is $\frac{g}{4}$ is

The mass of a planet is $\frac{1}{9}$ of the mass of the Earth and its radius is half that of the Earth. If a body weighs $9 \ N$ on the Earth,its weight on the planet would be ........ $N$.

$A$ planet of radius $R = \frac{1}{10} \times$ (radius of Earth) has the same mass density as Earth. Scientists dig a well of depth $\frac{R}{5}$ on it and lower a wire of the same length and of linear mass density $\lambda = 10^{-3} \ kg \ m^{-1}$ into it. If the wire is not touching anywhere,the force applied at the top of the wire by a person holding it in place is (take the radius of Earth $= 6 \times 10^6 \ m$ and the acceleration due to gravity on Earth $g_e = 10 \ m \ s^{-2}$) (in $N$)

In the provided figure of the Earth,the value of acceleration due to gravity is the same at points $A$ and $C$,but it is smaller than its value at point $B$ (surface of the Earth). The value of $OA : AB$ is $x : y$. The value of $x$ is $\ldots \ldots \ldots$

How does the acceleration due to gravity $(g)$ at a location on Earth change with latitude?

The mass of the earth is $81$ times that of the moon and the radius of the earth is $3.5$ times that of the moon. The ratio of the acceleration due to gravity at the surface of the moon to that at the surface of the earth is