Two spherical bodies of mass $M$ and $5M$ and radii $R$ and $2R$ are released in free space with initial separation between their centres equal to $12R.$ If they attract each other due to gravitational force only,then the distance covered by the smaller body before collision is (in $R$)

The figure shows the variation of the gravitational acceleration $a_g$ of four planets with the radial distance $r$ from the center of the planet for $r \ge R$ (where $R$ is the radius of the planet). Plots $1$ and $2$ coincide for $r \ge R_2$,and plots $3$ and $4$ coincide for $r \ge R_4$. The sequence of the planets in the descending order of their densities is:

$Assertion$ : The length of the day is slowly increasing.
$Reason$ : The dominant effect causing a slowdown in the rotation of the earth is the gravitational pull of other planets in the solar system.

$A$ man of mass $m$ starts falling towards a planet of mass $M$ and radius $R.$ As he reaches near to the surface,he realizes that he will pass through a small hole in the planet. As he enters the hole,he sees that the planet is really made of two pieces: a spherical shell of negligible thickness of mass $\frac{2M}{3}$ and a point mass $\frac{M}{3}$ at the centre. The change in the force of gravity experienced by the man is:

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

Three point masses,each of mass $m$,are kept at the corners of an equilateral triangle of side $L$. The system rotates about the center of the triangle without any change in the separation of masses during rotation. The period of rotation is directly proportional to