A body weighs 144 N at the surface of earth. When it is taken to a height of h=3R, where R is radius of earth, it would weigh

Options

A. 48 N
B. 39 N
C. 16 N
D. 9 N

Answer

To solve the problem of finding the weight of a body at a height of \( h = 3R \) (where \( R \) is the radius of the Earth), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Weight at the Surface of the Earth**:
The weight of the body at the surface of the Earth is given as \( W = 144 \, \text{N} \).

2. **Identify the Height**:
The height \( h \) at which we need to find the weight is \( h = 3R \).

3. **Use the Formula for Weight Variation**:
The weight of an object at a height \( h \) above the surface of the Earth can be calculated using the formula:
\[ W' = W \left( \frac{1}{(1 + \frac{h}{R})^2} \right) \]
where \( W' \) is the weight at height \( h \), and \( W \) is the weight at the surface.

4. **Substitute the Values**:
Here, \( h = 3R \), so we can substitute this into the formula:
\[ W' = 144 \left( \frac{1}{(1 + \frac{3R}{R})^2} \right) \]
Simplifying the expression inside the parentheses:
\[ W' = 144 \left( \frac{1}{(1 + 3)^2} \right) = 144 \left( \frac{1}{4^2} \right) = 144 \left( \frac{1}{16} \right) \]

5. **Calculate the New Weight**:
Now, we calculate \( W' \):
\[ W' = \frac{144}{16} = 9 \, \text{N} \]

### Final Answer:
Thus, the weight of the body at a height of \( h = 3R \) is \( \boxed{9 \, \text{N}} \).