If the radius of the Earth becomes $n$ times its present value,without any change in its mass,then the duration of the day becomes:

Two identical thin uniform rods of mass $M$ and length $L$ are placed in a line at a separation of $L$. Find the gravitational force acting between them.

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

$A$ tunnel is dug in the Earth across one of its diameters. Two masses $m$ and $2m$ are dropped from the ends of the tunnel. The masses collide, stick to each other, and perform $S.H.M.$ The amplitude of the $S.H.M.$ will be:

The correct graph representing the variation of total energy $(E_t)$,kinetic energy $(E_k)$,and potential energy $(U)$ of a satellite with its distance $(r)$ from the centre of the Earth is:

When a satellite in a circular orbit around the earth enters the atmospheric region,it encounters small air resistance to its motion. Then