Calculate the depth below the surface of the earth where the acceleration due to gravity is 2% of its value at the earth's surface.
Take, Radius of earth = 6,400 km

Explanation

To find the depth below the surface of the Earth where the acceleration due to gravity is 2% of its value at the Earth's surface, we can follow these steps:

### Step 1: Understand the formula for gravity at depth
The acceleration due to gravity at a depth \( d \) below the surface of the Earth is given by the formula:
\[ g' = g \left(1 - \frac{d}{R_e}\right) \]
where:
- \( g' \) is the acceleration due to gravity at depth \( d \),
- \( g \) is the acceleration due to gravity at the surface,
- \( R_e \) is the radius of the Earth.

### Step 2: Set up the equation for 2% of surface gravity
We need to find the depth \( d \) where \( g' = 0.02g \) (which is 2% of \( g \)). Thus, we can set up the equation:
\[ 0.02g = g \left(1 - \frac{d}{R_e}\right) \]

### Step 3: Simplify the equation
Dividing both sides by \( g \) (assuming \( g \neq 0 \)):
\[ 0.02 = 1 - \frac{d}{R_e} \]

### Step 4: Rearrange the equation to solve for \( d \)
Rearranging the equation gives:
\[ \frac{d}{R_e} = 1 - 0.02 \]
\[ \frac{d}{R_e} = 0.98 \]

### Step 5: Solve for \( d \)
Now, multiplying both sides by \( R_e \):
\[ d = 0.98 R_e \]
Given that the radius of the Earth \( R_e = 6400 \) km, we can substitute this value:
\[ d = 0.98 \times 6400 \text{ km} \]

### Step 6: Calculate the depth
Calculating the value:
\[ d = 6272 \text{ km} \]

### Final Answer
The depth below the surface of the Earth where the acceleration due to gravity is 2% of its value at the Earth's surface is **6272 km**.

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