The weight of a body on the suface of the earth is 100 N. The same at a height equal to a radius of the earth will be

Options

A. 25 N
B. 40 N
C. 75 N
D. 100 N

Explanation

To solve the problem step by step, we will use the concept of gravitational force and how it changes with height.

### Step 1: Understand the weight of the body on the surface of the Earth
The weight \( W \) of a body on the surface of the Earth is given as 100 N. The weight is defined as:
\[ W = m \cdot g \]
where \( m \) is the mass of the body and \( g \) is the acceleration due to gravity at the surface of the Earth, which is approximately \( 9.8 \, \text{m/s}^2 \).

### Step 2: Calculate the mass of the body
From the equation \( W = m \cdot g \), we can rearrange it to find the mass \( m \):
\[ m = \frac{W}{g} = \frac{100 \, \text{N}}{9.8 \, \text{m/s}^2} \approx 10.20 \, \text{kg} \]

### Step 3: Determine the gravitational acceleration at height equal to the radius of the Earth
When the body is taken to a height \( h \) equal to the radius of the Earth \( R \), the new gravitational acceleration \( g_h \) can be calculated using the formula:
\[ g_h = \frac{g}{(1 + \frac{h}{R})^2} \]
Since \( h = R \), we have:
\[ g_h = \frac{g}{(1 + 1)^2} = \frac{g}{4} = \frac{9.8 \, \text{m/s}^2}{4} \approx 2.45 \, \text{m/s}^2 \]

### Step 4: Calculate the weight of the body at the new height
Now, we can find the weight \( W_h \) of the body at this height:
\[ W_h = m \cdot g_h = 10.20 \, \text{kg} \cdot 2.45 \, \text{m/s}^2 \approx 25 \, \text{N} \]

### Conclusion
The weight of the body at a height equal to the radius of the Earth is approximately **25 N**.

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