The period of revolution of a satellite orbiting Earth at a height $4\mathrm{R}$ above the surface of Earth is $x \mathrm{hrs}$, where $R$ is the radius of earth. The period of another satellite at a height $1.5\mathrm{R}$ from the surface of the Earth is

A planet is revolving around the sun in an elliptical orbit. If the speed of planet at shown position $P$ ($M$:Mass of Sun) is $\sqrt{\frac{kGM}{2\mathrm{a}}}$, then value of $k$ is ______.

A ring of mass $M$ and radius $R$ is fixed and a point mass $m$ is released from rest as shown in figure. If speed of the particle when it reaches the centre of the ring is $\sqrt{\left(k-\frac{k}{\sqrt{3}}\right)\frac{GM}{R}}$, then value of $k$ is ______.