Physics - Gravitation Question with Solution | TestHub

PhysicsGravitationField & ForceEasy2 minPYQ_2020

PhysicsEasysingle choice

The radii of two planets are $R_{1}$ and $R_{2}$ and their densities are $ρ_{1}$ and $ρ_{2}$ respectively. If $g_{1}$ and $g_{2}$ represent the acceleration due to gravity at their respective surfaces, then $\frac{g_{1}}{g_{2}}$ is

Options:

Answer:

Solution:

The value of $g$ at surface

$g = \frac{{Gm}_{e}}{R_{e}^{2}} = \frac{G}{R_{e}^{2}} . \frac{4π}{3} R_{e}^{3} ρ$

$g = \frac{4}{3} π G R ρ$

So, $\frac{g_{1}}{g_{2}} = \frac{\frac{4}{3} π G R_{1} ρ_{1}}{\frac{4}{3} π G R_{2} ρ_{2}} \Rightarrow \frac{g_{1}}{g_{2}} = \frac{R_{1} ρ_{1}}{R_{2} ρ_{2}}$

Subject:PhysicsTopic:GravitationSubtopic:Field & Force

⏱ 2mℹ️ Source: PYQ_2020

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