A particle is projected vertically upward with velocity $\sqrt{\frac{2}{3}\frac{GM}{R}}$ from the surface of Earth. The height attained by it is ($G, M, R$ have usual meanings)

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 ______.