Physics - Gravitation Question with Solution | TestHub

PhysicsGravitationAcceleration Due to GravityMedium2 minPYQ_2021

PhysicsMediumsingle choice

If $R_{E}$ be the radius of Earth, then the ratio between the acceleration due to gravity at a depth $r$ below and a height $r$ above the earth surface is:
(Given : $r < R_{E}$ )

Options:

Answer:

Solution:

$\frac{g_{h}}{g_{d}} = \frac{\frac{G M}{{(R_{E} + r)}^{2}}}{\frac{G M}{R_{E}^{3}} (R_{E} - r)} = \frac{R_{E}^{3}}{{(R_{E} + r)}^{2} (R_{E} - r)}$
$\frac{g_{d}}{g_{h}} = \frac{{(R_{E} + r)}^{2} (R_{E} - r)}{R_{E}^{3}} = \frac{R_{E}^{3} - R_{E} r^{2} + r R_{E}^{2} - r^{3}}{R_{E}^{3}} = 1 - \frac{r^{2}}{R_{E}^{2}} + \frac{r}{R_{E}} - {(\frac{r}{R_{E}})}^{3}$

Stream:JEESubject:PhysicsTopic:GravitationSubtopic:Acceleration Due to Gravity

⏱ 2mℹ️ Source: PYQ_2021

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