When a satellite in a circular orbit around the earth enters the atmospheric region,it encounters small air resistance to its motion. Then

Inside a uniform spherical shell:
$(a)$ The gravitational field is zero.
$(b)$ The gravitational potential is zero.
$(c)$ The gravitational field is same everywhere.
$(d)$ The gravitational potential is same everywhere.
$(e)$ All of the above.
Choose the most appropriate answer from the options given below:

Weighing the Earth: You are given the following data: $g = 9.81 \; m/s^2$, $R_E = 6.37 \times 10^6 \; m$, the distance to the moon $R = 3.84 \times 10^8 \; m$, and the time period of the moon's revolution is $27.3$ days. Obtain the mass of the Earth $M_E$ in two different ways.

Statement $(A)$ Two artificial satellites revolving in the same circular orbit have the same period of revolution.
Statement $(B)$ The orbital velocity is inversely proportional to the square root of the radius of the orbit.
Statement $(C)$ The escape velocity of a body is independent of the altitude of the point of projection.

$A$ solid sphere of radius $R$ gravitationally attracts a particle of mass $m$ placed at a distance of $3R$ from its centre with a force $F_{1}$. Now,a spherical cavity of radius $\frac{R}{2}$ is made in the sphere (as shown in the figure) such that the cavity is tangent to the centre of the sphere and the outer surface. The force on the particle becomes $F_{2}$. The value of $F_{1} : F_{2}$ is:

The variation of acceleration due to gravity $g$ with distance $d$ from the centre of the earth is best represented by ($R =$ Earth's radius)