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)

Particles of mass $100 \, g$ each are placed at the vertices of an equilateral triangle of side $20 \, cm$. How much work must be done to increase the separation between them to infinity?

Two particles of equal mass $(m)$ each move in a circle of radius $(r)$ under the action of their mutual gravitational attraction. Find the speed of each particle.

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 ............ .

Three particles of equal mass $m$ are situated at the vertices of an equilateral triangle of side $l$. They are moving in a circle under the influence of their mutual gravitational interaction. Then their time period of revolution is directly proportional to

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