The mass of a hypothetical planet is 1/100 that of Earth and its radius is 1/4 that of Earth. If a person weighs 600 N on Earth, what would he weigh on this planet?

Options

A. 24 N
B. 48 N
C. 96 N
D. 192 N

Explanation

To solve the problem, we need to find the weight of a person on a hypothetical planet given the mass and radius of the planet compared to Earth.

### Step-by-step Solution:

1. **Understand the weight formula**:
The weight \( W \) of an object is given by the formula:
\[ W = \frac{G \cdot m \cdot M}{R^2} \]
where \( G \) is the gravitational constant, \( m \) is the mass of the object, \( M \) is the mass of the planet, and \( R \) is the radius of the planet.

2. **Identify the parameters**:
- Mass of the hypothetical planet \( M_p = \frac{1}{100} M_e \) (where \( M_e \) is the mass of Earth)
- Radius of the hypothetical planet \( R_p = \frac{1}{4} R_e \) (where \( R_e \) is the radius of Earth)
- Weight of the person on Earth \( W_e = 600 \, \text{N} \)

3. **Weight on Earth**:
The weight of the person on Earth can be expressed as:
\[ W_e = \frac{G \cdot m \cdot M_e}{R_e^2} \]
We know \( W_e = 600 \, \text{N} \).

4. **Weight on the hypothetical planet**:
The weight of the person on the hypothetical planet can be expressed as:
\[ W_p = \frac{G \cdot m \cdot M_p}{R_p^2} \]
Substituting \( M_p \) and \( R_p \):
\[ W_p = \frac{G \cdot m \cdot \left(\frac{1}{100} M_e\right)}{\left(\frac{1}{4} R_e\right)^2} \]

5. **Simplifying the expression**:
\[ W_p = \frac{G \cdot m \cdot \left(\frac{1}{100} M_e\right)}{\left(\frac{1}{16} R_e^2\right)} = \frac{G \cdot m \cdot M_e}{R_e^2} \cdot \frac{1}{100} \cdot 16 \]
\[ W_p = W_e \cdot \frac{16}{100} \]

6. **Substituting the known weight**:
\[ W_p = 600 \, \text{N} \cdot \frac{16}{100} = 600 \, \text{N} \cdot 0.16 \]

7. **Calculating the final weight**:
\[ W_p = 96 \, \text{N} \]

### Conclusion:
The weight of the person on the hypothetical planet would be **96 N**.