JEE Main · 2019 · 09 Apr 2019 · Shift 1 · Gravitation

The field at a point depends only on the mass lying inside that radius, by the shell theorem. At a distance $3a$ from the centre the whole solid sphere (mass $M$, radius $a$) and the whole surrounding shell (mass $2M$, outer radius $3a$) are enclosed, so the mass that matters is $M+2M=3M$. Treating it as a point mass at the centre, $g=\frac{G{M}_{enc}}{r^2}=\frac{G(3M)}{(3a{)}^2}=\frac{3GM}{9a^2}=\frac{GM}{3a^2}$.