A solid sphere of radius R gravitationally attracts a particle...

Let the initial mass of the sphere is $m ' .$ Hence, mass of
a removed portion will be $m ' / 8$,${F}_{1} = m . E . = \dfrac{m . Gm '}{9R^{2}}$

${F}_{2} = m\left[\dfrac{G \cdot m '}{\left(3R\right)2} - \dfrac{G \cdot m ' / 8}{\left(5R / 2\right)2}\right]= \dfrac{Gm '}{9R^{2}} - \dfrac{Gm ' \times 4}{8 \times 25}= \left(\dfrac{1}{9} - \dfrac{1}{50}\right)\dfrac{Gm '}{R2}$

${F}_{2} = \dfrac{41}{50 \times 9} \cdot \dfrac{Gm '}{R2}⇒ \dfrac{F1}{F2} = \dfrac{1}{9} \times \dfrac{50 \times 9}{41} = \dfrac{50}{41}$