State whether the following statements are true or false:
$(a)$ The intensity of the Earth's gravitational field increases as we move higher above the Earth's surface.
$(b)$ There is no atmosphere on the Moon because the escape velocity on the Moon is small.
$(c)$ $A$ satellite orbiting the Earth is in a state of weightlessness.

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 ..........

State whether the following statements are true or false:
$(a)$ The value of acceleration due to gravity increases as we go to a depth $d$ below the Earth's surface.
$(b)$ If the escape velocity for an object of mass $m$ on the Earth's surface is $11.2 \, km/s$,then the escape velocity for an object of mass $2m$ is $22.4 \, km/s$.
$(c)$ If the Earth's gravitational attraction suddenly disappears,the mass of an object becomes zero,but its weight remains the same.

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:

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)

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