question_answer

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.                                                  

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) \[\frac{1}{2}G\pi \rho \vec{\ell }\]

Correct Answer: A

Solution :

[a] For calculation of gravitational field intensity inside the cavity. \[{{\vec{I}}_{1}}=\frac{G\left( \frac{4}{3}\pi {{R}_{1}}^{3} \right)\rho \left( -{{{\vec{r}}}_{1}} \right)}{{{R}_{1}}^{3}}\] \[{{\vec{I}}_{2}}=\frac{G\left( \frac{4}{3}\pi {{R}_{2}}^{3} \right)\rho \left( -{{{\vec{r}}}_{2}} \right)}{{{R}_{2}}^{3}}\] \[\vec{I}={{\vec{I}}_{1}}-{{\vec{I}}_{2}}\](\[\vec{I}-\] intensity inside the cavity)