A body of weight 72 N moves from the surface of earth at a height half of the radius of earth , then geavitational force exerted on it will be

Options

A. 36 N
B. 32 N
C. 144 N
D. 50 N

Answer

To solve the problem, we need to find the gravitational force acting on a body when it is moved to a height that is half of the Earth's radius. Let's break it down step by step.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Weight of the body (W) = 72 N
- Height (h) = \( \frac{R_e}{2} \) where \( R_e \) is the radius of the Earth.

2. **Understand the Relationship Between Weight and Mass:**
- Weight (W) is given by the formula:
\[ W = mg \]
- Here, \( m \) is the mass of the body and \( g \) is the acceleration due to gravity at the surface of the Earth.

3. **Calculate the Mass of the Body:**
- Rearranging the weight formula gives:
\[ m = \frac{W}{g} \]
- We will keep \( m \) in terms of \( g \) for now.

4. **Determine the New Acceleration Due to Gravity (g'):**
- The formula for gravitational acceleration at a height \( h \) above the Earth's surface is:
\[ g' = g \left( \frac{R_e}{R_e + h} \right)^2 \]
- Substituting \( h = \frac{R_e}{2} \):
\[ g' = g \left( \frac{R_e}{R_e + \frac{R_e}{2}} \right)^2 \]
\[ = g \left( \frac{R_e}{\frac{3R_e}{2}} \right)^2 \]
\[ = g \left( \frac{2}{3} \right)^2 \]
\[ = g \cdot \frac{4}{9} \]

5. **Calculate the New Gravitational Force (F'):**
- The new gravitational force can be calculated using:
\[ F' = mg' \]
- Substituting \( g' \):
\[ F' = m \cdot \left( \frac{4}{9}g \right) \]
- Since \( mg = W = 72 \, \text{N} \):
\[ F' = \frac{4}{9} \cdot 72 \]
- Performing the calculation:
\[ F' = 32 \, \text{N} \]

### Final Answer:
The gravitational force exerted on the body at the height of half the radius of the Earth is **32 N**.

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