Question

if the gravitational field strength at a height h above the earth of radius R is same as at a depth of R/2 then h has value​

Answer 1

Answer:

$h=\frac{R}{4}$

Explanation:

$</p><p>\text { Variation in acceleration due to gravity, }\\</p><p>g^{\prime}=g\left(1-\frac{2 h}{R}\right) \text { and } g^{\prime}=g\left(1-\frac{d}{R}\right)\\</p><p>d=\frac{R}{2} ; \text { Here } g\left(1-\frac{2 h}{R}\right)=g\left(1-\frac{R / 2}{R}\right)\\</p><p>1-\frac{2 h}{R}=1-\frac{1}{2}=\frac{1}{2} \Rightarrow 1-\frac{1}{2}=\frac{2 h}{R}\\</p><p>\Rightarrow \frac{1}{2}=\frac{2 h}{R} \Rightarrow h=\frac{R}{4}</p><p>$

Answered by gauthmath