Search any question & find its solution
Question:
Answered & Verified by Expert
Acceleration due to gravity at a height \(h\) is equal to that at a depth \(d\) below the surface of the earth, if
Options:
Solution:
1635 Upvotes
Verified Answer
The correct answer is:
\(d=2 h\)
According to question,
Acceleration due to gravity at a height \((h)=\)
Acceleration due to gravity below depth \((d)\)
\(\begin{array}{llll}
\Rightarrow & g\left(1-\frac{2 h}{R_e}\right) =g\left(1-\frac{d}{R_e}\right) \\
\Rightarrow & 1-\frac{2 h}{R_e} =1-\frac{d}{R_e} \Rightarrow \frac{2 h}{R_e}=\frac{d}{R_e} \\
\Rightarrow & 2 h =d
\end{array}\)
Acceleration due to gravity at a height \((h)=\)
Acceleration due to gravity below depth \((d)\)
\(\begin{array}{llll}
\Rightarrow & g\left(1-\frac{2 h}{R_e}\right) =g\left(1-\frac{d}{R_e}\right) \\
\Rightarrow & 1-\frac{2 h}{R_e} =1-\frac{d}{R_e} \Rightarrow \frac{2 h}{R_e}=\frac{d}{R_e} \\
\Rightarrow & 2 h =d
\end{array}\)
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.