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Physics - Gravitation Question with Solution | TestHub

PhysicsGravitationField & ForceMedium2 minQB

PhysicsMediuminteger

For a planet of mass density $ρ = ρ_{0} r (ρ_{0} =$ constant, $r =$ distance from centre $)$ and radius R, ratio of acceleration due to gravity at surface to acceleration due to gravity at $r = R /3$ is $____$ .

Answer:

Solution:

Field inside at radius r: $E (r) = \frac{G \int _{0}^{r} ρ _{0} r 4 π r ^{2} d r}{r ^{2}} = \frac{G ρ _{0} 4 π r ^{2}}{4} = G ρ_{0} π r^{2}$

$g_{s u r f a ce} = G ρ_{0} π R^{2}, g (\frac{R}{3}) = G ρ_{0} π \frac{R ^{2}}{9}$

$\frac{g _{s u r f a ce}}{g _{R /3}} = 9$

Stream:JEESubject:PhysicsTopic:GravitationSubtopic:Field & Force

⏱ 2mℹ️ Source: QB

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