Two satellites of masses $m$ and $1.5 m$ are revolving around the earth in two circular orbits of heights $R_E$ and $2 R_E$ respectively,where $R_E$ is the radius of the earth. The ratio of the minimum and maximum gravitational forces exerted by the two satellites on the earth is

$A$ spherical body of radius $R$ consists of a fluid of constant density $\rho$ and is in equilibrium under its own gravity. If $P(r)$ is the pressure at a distance $r$ from the center $(r < R)$,then the correct option$(s)$ is(are):
$(A) P(r=0) = P_c$ (maximum pressure at center)
$(B) \frac{P(r=3R/4)}{P(r=2R/3)} = \frac{63}{80}$
$(C) \frac{P(r=3R/5)}{P(r=2R/5)} = \frac{16}{21}$
$(D) \frac{P(r=R/2)}{P(r=R/3)} = \frac{20}{27}$

The orbital velocity of a body near the surface of a planet $A$ is equal to the escape velocity of a body from the planet $B$. If the masses of planets $A$ and $B$ are the same,the ratio of their radii is

$A$ hemispherical shell of mass $2M$ and radius $6R$ and a point mass $M$ are performing circular motion due to their mutual gravitational interaction. Their positions are shown in the figure at any moment of time during motion. If $r_1$ and $r_2$ are the radii of the circular paths of the hemispherical shell and the point mass respectively,and $\omega_1$ and $\omega_2$ are the angular speeds of the hemispherical shell and the point mass respectively,then choose the correct option.

Four similar particles of mass $m$ are orbiting in a circle of radius $r$ in the same angular direction because of their mutual gravitational attractive force. The velocity of a particle is given by

$A$ person whose mass is $100\, {kg}$ travels from Earth to Mars in a spaceship. Neglect all other objects in the sky and take acceleration due to gravity on the surface of the Earth and Mars as $10\, {m/s^2}$ and $4\, {m/s^2}$ respectively. Identify from the below figures,the curve that fits best for the weight of the passenger as a function of time.