A body has a weight 72 N. When it is taken to a height `h=R`= radius of earth, it would weight

Options

A. 72 N
B. 36 N
C. 18 N
D. zero

Explanation

To solve the problem, we need to determine the weight of a body when it is taken to a height equal to the radius of the Earth (h = R).

### Step-by-Step Solution:

1. **Understanding Weight and Gravitational Force**:
The weight of a body (W) is given by the formula:
\[ W = mg \]
where \( m \) is the mass of the body and \( g \) is the acceleration due to gravity at the surface of the Earth.

2. **Given Information**:
The weight of the body at the surface of the Earth is given as:
\[ W = 72 \, \text{N} \]

3. **Finding the Mass of the Body**:
We can find the mass of the body using the weight formula. Rearranging the formula gives:
\[ m = \frac{W}{g} \]
However, we do not need to calculate the mass directly since we will use the ratio of gravitational forces.

4. **Effect of Height on Gravitational Force**:
When the body is taken to a height \( h = R \) (where \( R \) is the radius of the Earth), the new acceleration due to gravity \( g' \) at that height can be calculated using the formula:
\[ g' = \frac{g}{(1 + \frac{h}{R})^2} \]
Substituting \( h = R \):
\[ g' = \frac{g}{(1 + 1)^2} = \frac{g}{2^2} = \frac{g}{4} \]

5. **Calculating the New Weight**:
The new weight \( W' \) at height \( h = R \) can be calculated as:
\[ W' = mg' = m \left(\frac{g}{4}\right) \]
Since \( W = mg \), we can substitute:
\[ W' = \frac{W}{4} = \frac{72 \, \text{N}}{4} = 18 \, \text{N} \]

6. **Final Answer**:
Therefore, the weight of the body when taken to a height equal to the radius of the Earth is:
\[ W' = 18 \, \text{N} \]