A small area is removed from a uniform spherical shell of mass M and radius R. Then the gravitatioinal field intensity near the hollow portion is

Options

A. `(GM)/(R^(2))`
B. `(GM)/(2R^(2))`
C. `(3GM)/(2R^(2))`
D. zero

Explanation

Consider a small area (shaded strip)
here `E_("self")=` gravitational field due to this strip
and `E_(ext)=` gravitational field due to the rest of spherical shell.
`E_("in")=` gravitational field just inside the strip due to whole shell.
`E_(out)=` gravitaional field just outside the strip due to whole shell.
`E_("in")=E_(ext)-E_("self")=0`
`impliesE_(ext)=E_(self)`
`E_(out)=E_(ext)+E_("self")=(GM)/(R^(2))impliesE_(ext)=(GM)/(2R^(2))`
After the shaded area has been removed there is no `E_("self")` and no `E_("self")` and only `E_(ext)` hence `E_("net")=E_(ext)=(GM)/(2R^(2))`