$A$ spacecraft travels in a straight line from the Earth to the Moon. How will its weight change during this journey?

The mass density of a spherical body is given by $\rho(r) = \frac{k}{r}$ for $r \leq R$ and $\rho(r) = 0$ for $r > R$,where $r$ is the distance from the centre. The correct graph that describes qualitatively the acceleration,$a$,of a test particle as a function of $r$ is

$A$ body situated on the surface of the earth becomes weightless at the equator when the rotational kinetic energy of the earth reaches a critical value '$K$'. The value of '$K$' is given by [$g$ = gravitational acceleration on earth's surface,$M$ = mass of the earth,and $R$ = radius of the earth].

The dependence of the intensity of the gravitational field $(E)$ of the Earth on the distance $(r)$ from the center of the Earth is correctly represented 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.

Two satellites $s_1$ and $s_2$ of equal masses revolve in the same sense around a heavy planet in coplanar circular orbits of radii $R$ and $4R$. Which of the following statements is correct?