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Physics - Gravitation Question with Solution | TestHub

PhysicsGravitationField & ForceMedium2 minQB

PhysicsMediumsingle choice

Density of a solid sphere of radius R is $ρ = ρ_{0} (1 + \frac{r}{R})$ at a distance r from the centre. Find magnitude of intensity of gravitational field at a distance $r = \frac{R}{2}$ from centre.

Options:

Answer:

Solution:

From Gauss law

$E .4 π r^{2} = 4 π G \int ρ dv \Rightarrow E = \frac{G}{r ^{2}} \int_{0}^{r} ρ_{0} (1 + \frac{r}{R}) .4 π r^{2} dr = \frac{G}{r ^{2}} .4 π ρ_{0} \int_{0}^{r} (r^{2} + \frac{r ^{3}}{R}) dr = \frac{4 π ρ _{0} G}{r ^{2}} \cdot (\frac{r ^{3}}{3} + \frac{r ^{4}}{4 R}) = 4 π ρ G (\frac{r}{3} + \frac{r ^{2}}{4 R}) at r = \frac{R}{2} E = 4 π ρ_{0} G (\frac{R}{6} + \frac{R}{16}) E = (\frac{11 π}{12}) ρ_{0} GR$

Stream:JEESubject:PhysicsTopic:GravitationSubtopic:Field & Force

⏱ 2mℹ️ Source: QB

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