Inside a uniform sphere of density rho there is a spherical cavity whose centre is a distance l from the centre of the sphere- Find the strength G of the gravitational field inside the cavity-

Question

Toppr Admin · Accepted Answer

Treating the cavity as negative mass of density $- ρ$ in a uniform sphere density $+ ρ$ and using the superposition principle, the sought field strength is,
$\to G =_{1} +_{2}$
or $\to G = - \frac{4}{3} π γ ρ_{+} + - \frac{4}{3} γ π (- ρ)_{-}$
(where $_{+}$ and $_{-}$ are the position vectors of an arbitrary point $P$ inside the cavity with respect to centre of sphere and cavity respectively.)
Thus $\to G = - \frac{4}{3} π γ ρ (_{+} -_{-}) = - \frac{4}{3} π γ ρ \to l$

Inside a uniform sphere of density ρ there is a spherical cavity whose centre is at a distance l from the centre of the sphere. Find the strength G of the gravitational field inside the cavity.

Inside a uniform sphere of density $ρ$ there is a spherical cavity whose centre is at a distance $l$ from the centre of the sphere. Find the strength $G$ of the gravitational field inside the cavity.