Question

The value of acceleration due to gravity at a depth of $1600\, km$ is equal to

• A. $9.8 \, ms^{-2}$
• B. $4.9 \, ms^{-2}$
• C. $19.6 \, ms^{-2}$
• D. $7.35\, ms^{-2}$

Answer 1

Answer: (D)

Given.
Depth $(d)=1600 \,km$
We know that,
$g_{d} =g\left(1-\frac{d}{R}\right) $
Here $g=9.8 \,m / s ^{2}$
$R=6400 \,km $
$g_{d} =g\left(1-\frac{1600}{6400}\right) $
$=9.8\left(1-\frac{1}{4}\right)$
$=9.8\left(\frac{4-1}{4}\right)=\frac{9.8 \times 3}{4} $
$g_{d} =7.35 \,ms ^{-2}$