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. Here’s a step-by-step breakdown of the solution:

### 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:
\[ W = mg \]
where \( m \) is the mass of the body and \( g \) is the acceleration due to gravity at the surface of the Earth.

Given that the weight \( W = 72 \, \text{N} \), we can express this as:
\[ 72 = mg \]

### Step 2: Determine the Gravitational Acceleration at Height \( h = R \)
When the body is taken to a height \( h \) equal to the radius of the Earth \( R \), the new gravitational acceleration \( g_h \) at that height can be calculated using the formula:
\[ g_h = \frac{GM}{(R + h)^2} \]
Since \( h = R \), we have:
\[ g_h = \frac{GM}{(R + R)^2} = \frac{GM}{(2R)^2} = \frac{GM}{4R^2} \]

### Step 3: Relate the New Gravitational Acceleration to the Surface Gravity
We know that the gravitational acceleration at the surface of the Earth \( g \) is given by:
\[ g = \frac{GM}{R^2} \]
Now, we can express \( g_h \) in terms of \( g \):
\[ g_h = \frac{g}{4} \]

### Step 4: Calculate the Weight at Height \( h = R \)
The weight of the body at height \( h \) is given by:
\[ W_h = mg_h \]
Substituting \( g_h \):
\[ W_h = m \left( \frac{g}{4} \right) \]

### Step 5: Substitute the Mass from the Surface Weight
From Step 1, we have \( mg = 72 \, \text{N} \). Therefore, we can express \( m \) as:
\[ m = \frac{72}{g} \]
Substituting this into the weight equation at height \( h \):
\[ W_h = \frac{72}{g} \left( \frac{g}{4} \right) = \frac{72}{4} = 18 \, \text{N} \]

### Conclusion
The weight of the body when taken to a height equal to the radius of the Earth is:
\[ W_h = 18 \, \text{N} \]