A body of 200 kg wt is lying in the surface the earth. Find its weight at a place 'R' above the surface of the earth (Radius of the earth is R),

Options

A. 25 kg wt
B. 100 kg wt
C. 50 kg wt
D. remains same

Explanation

To find the weight of a body at a height 'h' above the surface of the Earth, we can use the formula for gravitational force. The weight of the body at height 'h' can be calculated using the following steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Weight of the body on the surface of the Earth, \( W = 200 \, \text{kg} \).
- Radius of the Earth, \( R \).
- Height above the surface of the Earth, \( h = R \).

2. **Understand the Weight on the Surface:**
- The weight of an object is given by the formula:
\[ W = mg \]
where \( m \) is the mass of the object and \( g \) is the acceleration due to gravity at the surface of the Earth.

3. **Calculate the Mass of the Body:**
- Since weight is given as 200 kg, we need to convert this to mass. Weight is measured in newtons (N), so we must use the weight in terms of force:
\[ W = 200 \, \text{kg} \times g \]
- Here, we can assume \( g \approx 9.81 \, \text{m/s}^2 \) (standard acceleration due to gravity).

4. **Determine the Weight at Height \( h \):**
- The formula for gravitational force at a height \( h \) above the surface of the Earth is:
\[ W' = \frac{mg}{(1 + \frac{h}{R})^2} \]
- Substituting \( h = R \):
\[ W' = \frac{mg}{(1 + 1)^2} = \frac{mg}{4} \]

5. **Calculate the New Weight:**
- Since \( W = mg \), we can substitute this into the equation:
\[ W' = \frac{W}{4} = \frac{200 \, \text{kg}}{4} = 50 \, \text{kg} \]

### Final Answer:
The weight of the body at a height \( R \) above the surface of the Earth is **50 kg**.