Gravitation question bank (Physics)

A satellite of mass $\frac{M}{2}$ is revolving around earth in a circular orbit at a height of $\frac{R}{3}$ from earth surface. The angular momentum of the satellite is $M \sqrt{\frac{G M R}{x}}$. The value of $x$ is ______ , where $M$ and $R$ are the mass and radius of earth, respectively. ( G is the gravitational constant)

A small point of mass $m$ is placed at a distance $2 R$ from the centre ' $O^{\prime}$ of a big uniform solid sphere of mass M and radius R . The gravitational force on ' m ' due to M is $\mathrm{F}_1$. A spherical part of radius $\mathrm{R} / 3$ is removed from the big sphere as shown in the figure and the gravitational force on m due to remaining part of M is found to be $\mathrm{F}_2$. The value of ratio $\mathrm{F}_1: \mathrm{F}_2$ is