Question

How far away from the surface of the earth, does the acceleration due to gravity will be reduced by $36\%$ of its value on the surface of the earth if the radius of the earth is $6400km$?

• A. $1200km$
• B. $1600km$
• C. $1750km$
• D. $2000km$

Answer 1

The correct option is B

$1600km$

Step 1: Given

The acceleration due to gravity is reduced by $36\%$.

The radius of earth: $R=6400km$.

Acceleration due to gravity is $g$.

Acceleration due to gravity after reduction is $g\text{'}$.

Step 2: Formula Used

The acceleration due to gravity $\left(g\text{'}\right)$ at a height $\left(H\right)$ above Earth's surface is given by $g\text{'}=g{\left(\frac{R}{R+H}\right)}^2$.

Step 3: Solution

Calculate the value of acceleration due to gravity after reduction.

$\begin{array}{rcl}g\text{'}& =& g-36\%g\\ & =& g-\frac{36}{100}g\\ & =& \frac{64}{100}g\end{array}$

Calculate the value of height by substituting the values in the formula.

$$\begin{gathered} g\text{'}=g{\left(\frac{R}{R+H}\right)}^2 \\ \Rightarrow \frac{64}{100}g=g{\left(\frac{6400}{6400+H}\right)}^2 \\ \Rightarrow \sqrt{\frac{64}{100}}=\sqrt{{\left(\frac{6400}{6400+H}\right)}^2} \\ \Rightarrow \frac{8}{10}=\frac{6400}{6400+H} \\ \Rightarrow 4\left(6400+H\right)=5\times 6400 \\ \Rightarrow 4H=6400 \\ \Rightarrow H=1600km \end{gathered}$$.

Hence, the correct option is option B.