If a person with a spring balance and a body hanging from it goes up and up in an aeroplane,then the reading of the weight of the body as indicated by the spring balance will

Mark the correct statement:
$(i)$ Escape velocity does not depend on the mass of the body.
$(ii)$ If the total energy of a satellite becomes positive,it escapes from the Earth.
$(iii)$ The orbit of a geostationary satellite is called a parking orbit.

Imagine a narrow tunnel between two diametrically opposite points of the Earth. $A$ particle of mass $m$ is released in this tunnel. The time period of oscillation is ..........

Two particles of equal mass $m$ each move in a circle of radius $r$ under the action of their mutual gravitational attraction. The time period of each particle is

The gravitational force acting on a particle,due to a solid sphere of uniform density and radius $R$,at a distance of $3 R$ from the centre of the sphere is $F_1$. $A$ spherical hole of radius $(R / 2)$ is now made in the sphere as shown in the figure. The sphere with hole now exerts a force $F_2$ on the same particle. The ratio of $F_1$ and $F_2$ is

$A$ binary star system consists of two stars $A$ (mass $M_A = 2.2 M_S$) and $B$ (mass $M_B = 11 M_S$),where $M_S$ is the mass of the Sun. They are separated by a distance $d$ and rotate about their common centre of mass,which is stationary. What is the ratio of the angular momentum of star $A$ to the angular momentum of star $B$ about the centre of mass?