A solid sphere of uniform density and radius R apies a grav force of attraction =F1 on a particle placed at A distance of 2R fro the centre of the sphere . A spherical cavity of radius R/2 is now made in the sphere which applies a force F2 on the same particle, FI/F2?

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Q. A solid sphere of uniform density and radius

R

applies a gravitational force of attraction equal to

F_{1}

on a particle placed at a distance

2 R

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

F_{2}

on the same particle. The ratio

F_{1} / F_{2}

A solid sphere of uniform density and radius R applies a gravitational force of attraction equal to F₁ on a particle placed at P, distance 2R from the centre O of the sphere. A spherical cavity of radius R/2 is now made in the sphere as shown in figure. The sphere with cavity now applies a gravitational force F₂on same particle placed at P. The ratio $\frac{F_{2}}{F_{1}}$ will be