1. Tardigrade
  2. Question
  3. Physics
  4. A solid sphere of uniform density and radius R exerts a gravitational force of attraction F 1 on a particle P, distant 2 R from the centre of the sphere. A spherical cavity of radius R / 2 is now formed in the sphere as shown in figure. The sphere with cavity now applies a gravitational force F 2 on the same particle P. Find the ratio F 2 / F 1.

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. A solid sphere of uniform density and radius $R$ exerts a gravitational force of attraction $F _{1}$ on a particle $P$, distant $2 R$ from the centre of the sphere. A spherical cavity of radius $R / 2$ is now formed in the sphere as shown in figure. The sphere with cavity now applies a gravitational force $F _{2}$ on the same particle $P$. Find the ratio $F _{2} / F _{1}$.Physics Question Image

Solution:

$F _{1}=\frac{ GMm }{4 R ^{2}}, F _{2}$
$=$ force due to whole sphere - force due to the sphere forming the cavity
$=\frac{ GMm }{4 R ^{2}}-\frac{ GMm }{18 R ^{2}}$
$\Rightarrow \frac{7 GMm }{36 R ^{2}}$
$\therefore \frac{ F _{2}}{ F _{1}}=\frac{7}{9}$