State two factors that determine whether a planet will have an atmosphere or not.

The masses of two fixed spheres are $M$ and $2M$ and the radius of each sphere is $R$. Their centres are $10R$ apart. The minimum speed with which a particle of mass $\frac{M}{10}$ be projected from the mid-point of the line joining the centres of the two spheres so that it escapes to infinity is . . . . . . .

If ${v_e}$ and ${v_o}$ represent the escape velocity and orbital velocity of a satellite corresponding to a circular orbit of radius $R$,then

If $M$ is the mass of a planet and $R$ is its radius,then in order to become a black hole (where $c$ is the speed of light),which condition must be satisfied?

If an object is projected vertically upwards with a speed equal to half the escape speed of Earth,then the maximum height attained by it is ($R$ is the radius of Earth).

The escape velocity of an atmospheric particle which is $1000 \, km$ above the Earth's surface is .......... $km/s$ (radius of Earth is $6400 \, km$ and $g = 9.8 \, m/s^2$).