A solid sphere of uniform density and radius R applies a gravitational force of attraction equal to $$F1$$ on a particle placed at a distance $$2R$$ from the centre of the sphere. A spherical cavity of radius $$R/2$$ is now made in the sphere as shown in the figure. The sphere with the cavity now applies a gravitational force $$F2$$ on the same particle. The ratio $$F1/F2$$ is

Question

Infinity Learn · Accepted Answer

Mass of the cavity $$=$$ $$M/8$$ if mass of the sphere $$=$$ M as volume of the cavity is $$1/8th$$ of the sphere.$$F2=GMm4R2$$−$$GMm832R2=GMmR214$$−$$118=GMmR29$$−$$236$$ $$=GMmR2736$$∴ $$F1F2=364$$×$$7=97$$

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