Two satellites of earth $S_1$ and $S_2$ are moving in the same orbit. The mass of $S_1$ is four times the mass of $S_2$. Which one of the following statement is true ?

A rocket is fired 'vertically' from the surface of mars with a speed of $2\; km s ^{-1}$. If $20 \%$ of its initial energy is lost due to martian atmospheric resistance, how far will the rocket go from the surface of mars before returning to it? Mass of mars $=6.4 \times 10^{23} \;kg$ radius of mars $=3395\; km ; G=6.67 \times 10^{-11}\; N m ^{2} kg ^{-2}$

A hole is drilled through the earth along a diameter Band a stone is dropped into it. The stone reaches at the centre of the earth, which of the following quantity remains constant

A body of mass ($2 {M}$) splits into four masses $\{{m}, {M}-{m}, {m}, {M}-{m}\}$, which are rearranged to form a square as shown in the figure. The ratio of $\frac{{M}}{{m}}$ for which, the gravitational potential energy of the system becomes maximum is ${x}: 1$. The value of $x$ is ….. .

An astronaut takes a ball of mass $m$ from earth to space. He throws the ball into a circular orbit about earth at an altitude of $318.5 \mathrm{~km}$. From earth's surface to the orbit, the change in total mechanical energy of the ball is $x \frac{\mathrm{GM}_e \mathrm{~m}}{21 R_e}$. The value of $x$ is (take $R_{\mathrm{e}}=6370 \mathrm{~km}$ ):