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Physics - Gravitation Question with Solution | TestHub

PhysicsGravitationField & ForceEasy2 minPYQ_2020

PhysicsEasysingle choice

The mass density of a spherical body is given by $ρ (r) = \frac{k}{r}$ for $r \leq R$ and $ρ (r) = 0$ for $r > R,$ where r is the distance from the centre. The correct graph that describes qualitatively the acceleration, a, of a test particle as a function of r is :

Options:

Answer:

Solution:

For Inside point $(r \leq R)$

$g = E = \frac{G}{r^{2}} \int_{0}^{r} (4 π r^{2} d r) (\frac{K}{r}) \frac{G K}{r^{2}} \times \frac{4 π r^{2}}{2} = 2 π G K = c o n s t a n t$

For outside point $(r > R)$

$E = g = \frac{G M}{r^{2}} = \frac{G}{r^{2}} \int_{0}^{R} (4 π r^{2} d r^{'}) (\frac{K}{r^{'}}) = \frac{4 π K G}{r^{2}} {[\frac{{r^{'}}^{2}}{2}]}_{0}^{R}$

$E = g = \frac{2 π K G}{r^{2}} R^{2}$

$E \propto \frac{1}{r^{2}}$

Subject:PhysicsTopic:GravitationSubtopic:Field & Force

⏱ 2mℹ️ Source: PYQ_2020

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