Gravitational potential at the centre of curvature of a hemispherical bowl of radius $\mathrm{R}$ and mass $\mathrm{M}$ is $\mathrm{V}$ :-

A small ball of mass ' $\text{m}$ ' is released at a height ' $\text{R}$ ' above the Earth surface, as shown in the figure. If the maximum depth of the hall to which it goes is $\mathrm{R}/2$ inside the Earth through a narrow grove before coming to rest momentarily. The grove, contain an ideal spring of spring constant $\mathrm{K}$and natural length $\mathrm{R}$, the value of $\text{K}$is $\text{(R}$ is radius of Earth and $\text{M}$ mass of Earth)

For the double star system, the two stars having masses ${\mathrm{m}}_1$ and ${\mathrm{m}}_2$ are separated by a distance $\mathrm{r}$. They are revolving about their common center of mass in radii $r_1$and $r_2$ respectively. Which of the following is/are incorrect?

In the given figure, $L=1\mathrm{m}$, if total gravitational force on $4 \mathrm{kg}$ mass is ${\overrightarrow{\mathrm{F}}}_1$ and on $2 \mathrm{kg}$ mass is${\overrightarrow{\mathrm{F}}}_2$, If the value of the ratio of $\left|\frac{{\overrightarrow{\mathrm{F}}}_1}{{\overrightarrow{\mathrm{F}}}_2}\right|$ is $\sqrt{\alpha }$, then what will be the value of $\alpha ?$