Question

What is the acceleration due to gravity at a height equal to $\frac{R}{2}$ from the Earth’s surface?

• A. $\frac{3g}{4}$
• B. $\frac{4g}{3}$
• C. $\frac{9g}{4}$
• D. $\frac{4g}{9}$

Answer 1

The correct option is D

$\frac{4g}{9}$

Step 1: Given data

Height(h) = $\frac{R}{2}$

Step 2: Formula used

We know,

Acceleration due to the gravity at some height is given as $g\text{'}=\frac{g}{{\left(1+{\displaystyle \frac{h}{R}}\right)}^2}$

Step 3: Find the acceleration due to gravity

According to the question, the height is $\frac{R}{2}$

Now,

$g\text{'}=\frac{g}{{\left(1+{\displaystyle \frac{{\displaystyle \frac{R}{2}}}{R}}\right)}^2}=\frac{g}{{\left(1+{\displaystyle \frac{1}{2}}\right)}^2}=\frac{4}{9}g$

Therefore the new acceleration due to gravity is $\frac{4}{9}$ of the original acceleration due to gravity.

Hence, the correct option is (D).