The interior structure of the Earth is layered in spherical shells, like an onion. Assume that a certain planet has similar interior structure of core and outer shell, as shown in the above figure. The radius of the core is $R$ and the inner and outer radii of the outer shell are $R$ and $2R,$ respectively. If the mass of the core is $M=4.1 \times 10^{24}\text{ kg}$ and that of the outer shell is $4M,$ what is the approximate gravitational acceleration of a particle which is at a distance of $R$ from the surface of the outer shell?

• The universal gravitational constant is $G=6.67 \times 10^{-11} \text{ N }\cdot\text{m}^2\text{/kg}^2.$
• $R = 5.5\times10^6$ m.