A spherical cave of radius R/2 was carved out from a uniform sphere of radius R and original mass M. the center of the cave is at R/2 from the center of the large sphere. Point P is at a distance 2R from the center the large sphere and on the joing line of the two centers. the gravitational field strength g at point P is

Options

A. `g=(GM)/(4R^(2))`
B. `g=(5GM)/(8R^(2))`
C. `g=(3GM)/(16R^(2))`
D. `g=(7GM)/(36R^(2))`

Answer

D

Explanation

`g=(GM)/((2R)^(2))-(G(M//8))/((3R//2)^(2))`