Assertion $(A):$ An astronaut in an orbiting space station above the earth experiences weightlessness.
Reason $(R):$ An object moving around the earth under the influence of earth's gravitational force is in a state of 'free fall'.

Three equal mass satellites $A, B,$ and $C$ are in coplanar orbits around a planet as shown in the figure. The magnitudes of the angular momenta of the satellites as measured about the planet are $L_A, L_B$,and $L_C$. Which of the following statements is correct?

$A$ particle of mass $m$ is under the influence of the gravitational field of a body of mass $M (\gg m)$. The particle is moving in a circular orbit of radius $r_0$ with time period $T_0$ around the mass $M$. Then,the particle is subjected to an additional central force,corresponding to the potential energy $V_c(r) = m \alpha / r^3$,where $\alpha$ is a positive constant of suitable dimensions and $r$ is the distance from the center of the orbit. If the particle moves in the same circular orbit of radius $r_0$ in the combined gravitational potential due to $M$ and $V_c(r)$,but with a new time period $T_1$,then $(T_1^2 - T_0^2) / T_1^2$ is given by [ $G$ is the gravitational constant.]

$A$ ball is dropped from a spacecraft revolving around the earth at a height of $120 \ km$. What will happen to the ball?

What is the effect on the time period of a satellite orbiting around the Earth if its height decreases?

$A$ satellite of the earth is revolving in a circular orbit with a uniform velocity $V$. If the gravitational force suddenly disappears,the satellite will