Physics - Gravitation Question with Solution | TestHub

PhysicsGravitationMiscellaneousEasy2 minPYQ_2020

PhysicsEasysingle choice

A hypothetical planet in the shape of a sphere is completely made of an incompressible fluid and has a mass $M$ and radius $R$ . If the pressure at the surface of the planet is zero, then the pressure at the centre of the planet is [ $G$ = universal constant of gravitation]

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Solution:

The pressure gradient at a distance $r$ from the centre of the spherical planet is

$\frac{d P}{d r} = - ρ g$ , where $g$ is the acceleration due to gravity at that point

$\frac{d P}{d r} = - (\frac{3 M}{4 π R^{3}}) (\frac{G M}{R^{3}} r)$

$d P = - (\frac{3 G M^{2}}{4 π R^{6}} r) d r$

$\int_{P}^{0} d P = - \frac{3 G M^{2}}{4 π R^{6}} \int_{0}^{R} r d r$

$P = \frac{3 G M^{2}}{8 π R^{4}}$

Stream:JEESubject:PhysicsTopic:GravitationSubtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2020

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