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Gravitation — Physics STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 SciencePhysicsGravitation4 Marks
Question
State the formula for acceleration due to gravity at depth ' $d$ ' and altitude ' $h$ ' Hence show that their ratio is equal to $\left(\frac{R-d}{R-2 h}\right)$ by assuming that the altitude is very small as compared to the radius of the Earth.
✓

Answer

For an object at depth d, acceleration due to gravity of the Earth is given by,
$
g_d=g\left(1-\frac{ d }{ R }\right)
$
2. Also, the acceleration due to gravity at smaller altitude $h$ is given by,
$
g _{ h }= g \left(1-\frac{2 h }{ R }\right)
$
3. Hence, dividing equation (1) by equation (2),
we get,
$
\begin{aligned}
\frac{g_d}{g_h} & =\frac{g\left(1-\frac{d}{R}\right)}{g\left(1-\frac{2 h}{R}\right)}=\frac{R-d}{R} \times \frac{R}{R-2 h} \\
\therefore \quad \frac{g_d}{g_h} & =\frac{R-d}{R-2 h}
\end{aligned}
$

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