Gravitational field due to ring at a distance
$d= \sqrt 3 R$ on its axis is
$E=\large\frac{GMd}{(R^2+d^2)^{3/2}}$
$\quad=\large\frac{{\sqrt 3}GM}{8R^2}$
Force on the sphere = mass of sphere $ \times $ E
$\quad=8ME$
$\quad=\large \frac{\sqrt 3 \;GM^2}{R^2}$
Hence d is the correct answer.