The period of a satellite, in a circular orbit near an equatorial plane, will not depend on

What should be the angular speed of earth, so that body lying on equator may appear weightlessness $ (g = 10\,m/{s^2},\,\,R = 6400\,km)$

A particle of mass $M$ is placed at the centre of a uniform spherical shell of mass $2M$ and radius $R$. The gravitational potential on  the surface of the shell is

The dependence of acceleration due to gravity $g$ on the distance $r$ from the centre of the earth assumed to be a sphere of radius $R$ of uniform density is as shown figure below

The correct figure is

A particle of mass $M$ is situated at the centre of a spherical shell of same mass and radius $a$. The gravitational potential at a point situated at $\frac {a}{2}$ distance from the centre, will be

A satellite in force free space sweeps stationary interplanetary dust at a rate of $\frac{d M}{d t}=\alpha v$ where $M$ is mass and $v$ is the speed of satellite and $\alpha$ is a constant. The acceleration of satellite is