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

The figure shows the variation of the gravitational acceleration $a_g$ of four planets with the radial distance $r$ from the center of the planet for $r \ge R$ (where $R$ is the radius of the planet). Plots $1$ and $2$ coincide for $r \ge R_2$,and plots $3$ and $4$ coincide for $r \ge R_4$. The sequence of the planets in the descending order of their densities is:

If the height of a satellite from the surface of the Earth is increased,then its

$A$ particle of mass $M$ is at a distance $a$ from the surface of a thin spherical shell of equal mass $M$ and radius $a$. Which of the following statements is correct regarding the gravitational field and potential inside the shell?

The figure shows the orbit of a planet $P$ around the sun $S.$ $AB$ and $CD$ are the minor and major axes of the ellipse,respectively. If $U$ is the potential energy and $K$ is the kinetic energy of the planet,then $|U| > |K|$ at:

$A$ spacecraft which is moving with a speed $u$ relative to the earth in the $x$-direction,enters the gravitational field of a much more massive planet which is moving with a speed $3u$ in the negative $x$-direction. The spacecraft exits following the trajectory as shown below. The speed of the spacecraft with respect to the earth a long time after it has escaped the planet's gravity is given by