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, we need to determine the weight of a body when it is taken to a height of \( h = 3R \) above the Earth's surface, where \( R \) is the radius of the Earth. The weight of the body at the surface of the Earth is given as 144 N.

### Step-by-Step Solution:

1. **Understanding Weight at the Surface:**
The weight of the body at the surface of the Earth is given by the formula:
\[ W = \frac{GMm}{R^2} \]
where:
- \( G \) is the gravitational constant,
- \( M \) is the mass of the Earth,
- \( m \) is the mass of the body,
- \( R \) is the radius of the Earth.

Given that \( W = 144 \, \text{N} \), we can express this as:
\[ \frac{GMm}{R^2} = 144 \]

2. **Calculating Weight at Height \( h = 3R \):**
When the body is taken to a height \( h = 3R \), the distance from the center of the Earth becomes:
\[ d = R + h = R + 3R = 4R \]

The weight of the body at this new height can be calculated using the formula:
\[ W' = \frac{GMm}{(4R)^2} \]

3. **Substituting the Values:**
We can simplify the expression for \( W' \):
\[ W' = \frac{GMm}{16R^2} \]

Now, we know from the surface weight that:
\[ \frac{GMm}{R^2} = 144 \]
Therefore, we can substitute this into the equation for \( W' \):
\[ W' = \frac{144}{16} \]

4. **Calculating the Final Weight:**
Now, performing the division:
\[ W' = 9 \, \text{N} \]

### Conclusion:
The weight of the body when taken to a height of \( 3R \) above the Earth's surface is \( 9 \, \text{N} \).

### Final Answer:
The body would weigh **9 N** at a height of \( 3R \).

---