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 $\_\_\_\_\_\_\_\_m{s}^{-2}.$

• A. $9.66$
• B. $7.64$
• C. $5.00$
• D. $3.1$

Answer 1

The correct option is A

$9.66$

Step 1: Given data

Height below the Earth surface, $d=100km$,

Assume, Radius of Earth $R=6400km$, and gravity of Earth $g=10m{s}^{-2}$,

Let gravitational acceleration is $g\text{'}$.

Step 2: Find the gravitational acceleration, $\mathit{g}\mathbf{\text{'}}$,

Let gravitational acceleration at a depth $d$, is $g\text{'}=g\left(1-\frac{d}{R}\right)$ [where, $R$ is radius of Earth]

$$\begin{gathered} \Rightarrow g\text{'}=10\left(1-\frac{100}{6400}\right) \\ \Rightarrow g\text{'}=9.66m{s}^{-2} \end{gathered}$$

Hence, the gravitational acceleration, $g\text{'}=9.66m{s}^{-2}.$

Therefore, option (A) is correct.