The height vertically above's surface at which the acceleration due to gravity becomes `1%` of its value at the suuface is

Options

A. 8 R
B. 9 R
C. 10 R
D. 20 R

Explanation

To solve the problem of finding the height above the Earth's surface where the acceleration due to gravity becomes 1% of its value at the surface, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem:**
We know that the acceleration due to gravity at the surface of the Earth is denoted as \( g \). We need to find the height \( h \) above the surface where the acceleration due to gravity \( g' \) becomes \( 1\% \) of \( g \). Mathematically, this can be expressed as:
\[ g' = \frac{g}{100} \]

2. **Using the Formula for Gravity at Height:**
The formula for the acceleration due to gravity at a height \( h \) above the Earth's surface is given by:
\[ g' = g \left( \frac{R}{R + h} \right)^2 \]
where \( R \) is the radius of the Earth.

3. **Setting Up the Equation:**
We substitute \( g' = \frac{g}{100} \) into the formula:
\[ \frac{g}{100} = g \left( \frac{R}{R + h} \right)^2 \]

4. **Cancelling \( g \):**
We can cancel \( g \) from both sides (assuming \( g \neq 0 \)):
\[ \frac{1}{100} = \left( \frac{R}{R + h} \right)^2 \]

5. **Cross-Multiplying:**
Cross-multiplying gives:
\[ 1 = 100 \left( \frac{R}{R + h} \right)^2 \]
Which simplifies to:
\[ (R + h)^2 = 100R^2 \]

6. **Taking the Square Root:**
Taking the square root of both sides:
\[ R + h = 10R \]

7. **Solving for \( h \):**
Rearranging the equation to find \( h \):
\[ h = 10R - R = 9R \]

### Final Answer:
The height \( h \) above the Earth's surface at which the acceleration due to gravity becomes \( 1\% \) of its value at the surface is:
\[ h = 9R \]