Question

Assuming earth to be a sphere of a uniform density, what is the value of gravitational acceleration in a mine $100km$ below the earth's surface $(\text{Given}R=6400km)$

• A. $5.06m/s^2$
• B. $7.64m/s^2$
• C. $9.66m/s^2$
• D. $3.10m/s^2$

Answer 1

The correct option is C $9.66m/s^2$

Formula used:
$g^{\prime }=g(1-\frac{d}{r})$
Given,
$d=100km$
$R=6400km$
Acceleration due to gravity at depth $d$,
$g^{\prime }=g[1-\frac{d}{r}]=g[1-\frac{100}{6400}]$

$=9.8[1-\frac{1}{64}]$
$=9.8\times \frac{63}{64}=9.66m/s^2$
Final Answer: (a)