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

Two bodies,each of mass $M$,are kept fixed with a separation $2L$. $A$ particle of mass $m$ is projected from the mid-point of the line joining their centres,perpendicular to the line. The gravitational constant is $G$. The correct statement$(s)$ is/are:
$(a)$ The minimum initial velocity of the mass $m$ to escape the gravitational field of the two bodies is $4 \sqrt{\frac{GM}{L}}$
$(b)$ The minimum initial velocity of the mass $m$ to escape the gravitational field of the two bodies is $2 \sqrt{\frac{GM}{L}}$
$(c)$ The minimum initial velocity of the mass $m$ to escape the gravitational field of the two bodies is $\sqrt{\frac{2GM}{L}}$
$(d)$ The energy of the mass $m$ remains constant

The variation of acceleration due to gravity $g$ with distance $d$ from the centre of the earth is best represented by ($R =$ Earth's radius)

Two identical particles of mass $1 \, kg$ each go round a circle of radius $R$,under the action of their mutual gravitational attraction. The angular speed of each particle is:

Fill in the blanks:
$(a)$ In the region inside the Earth,the acceleration due to gravity is proportional to the distance from the center of the Earth as ..... .
$(b)$ If the Earth shrinks such that its radius becomes half and its mass remains constant,the weight of an object on the Earth increases by a factor of ......... .
$(c)$ The orbital velocity of a geostationary satellite of the Earth is approximately ............ .