Acceleration due to gravity at a height \(h\) is equal to that at a depth \(d\) below the surface of the…
Acceleration due to gravity at a height \(h\) is equal to that at a depth \(d\) below the surface of the earth, if
\(d=h\)
\(2 d=h\)
\(d=2 h\)
\(3 d=h\)
Solution
According to question,
Acceleration due to gravity at a height \((h)=\)
Acceleration due to gravity below depth \((d)\)
\(\begin{array}{llll}
\Rightarrow & g\left(1-\frac{2 h}{R_e}\right) =g\left(1-\frac{d}{R_e}\right) \\
\Rightarrow & 1-\frac{2 h}{R_e} =1-\frac{d}{R_e} \Rightarrow \frac{2 h}{R_e}=\frac{d}{R_e} \\
\Rightarrow & 2 h =d
\end{array}\)