Gravitation Question 340
Question: Inside a uniform sphere of density p there is a spherical cavity whose centre is at a distance $ [\ell ] $ from the centre of the sphere. Find the strength F of the gravitational field inside the cavity at the point P.
Options:
A) $ [\frac{4}{3}G\pi \rho \vec{\ell }] $
B) $ [\frac{1}{3}G\pi \rho \vec{\ell }] $
C) $ [\frac{2}{3}G\pi \rho \vec{\ell }] $
D) $ [\frac{1}{2}G\pi \rho \vec{\ell }] $
Show Answer
Answer:
Correct Answer: A
Solution:
-
For calculation of gravitational field intensity inside the cavity. $ [{\vec I _{1}}=\frac{G(\frac{4}{3}\pi R _{1}^{3})\rho (-{{\vec r} _{1}} )}{R _{1}^{3}}] $
$ [{\vec I _{2}}=\frac{G( \frac{4}{3}\pi R _{2}^{3} )\rho ( -{{\vec r} _{2}} )}{R _{2}^{3}}] $
$ [\vec{I}={\vec I _{1}}-{\vec I _{2}}] $ ($ [\vec{I}-] $ intensity inside the cavity)
