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 determine the weight of a person on a hypothetical planet given the mass and radius of that planet in relation to Earth.

### Step-by-step Solution:

1. **Identify the Given Values:**
- 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, \( W_e = 600 \, \text{N} \)

2. **Weight on Earth:**
The weight of a person on Earth is given by the formula:
\[ W_e = m \cdot g_e \]
where \( g_e \) is the acceleration due to gravity on Earth. We can express \( g_e \) as:
\[ g_e = \frac{G M_e}{R_e^2} \]
Here, \( G \) is the gravitational constant.

3. **Weight on the Hypothetical Planet:**
The weight of the person on the hypothetical planet can be expressed as:
\[ W_p = m \cdot g_p \]
where \( g_p \) is the acceleration due to gravity on the hypothetical planet. We can express \( g_p \) as:
\[ g_p = \frac{G M_p}{R_p^2} \]

4. **Substituting the Mass and Radius:**
Substitute \( M_p \) and \( R_p \) into the equation for \( g_p \):
\[ g_p = \frac{G \left(\frac{1}{100} M_e\right)}{\left(\frac{1}{4} R_e\right)^2} \]
Simplifying the denominator:
\[ g_p = \frac{G \left(\frac{1}{100} M_e\right)}{\frac{1}{16} R_e^2} = \frac{G M_e}{100} \cdot \frac{16}{R_e^2} = \frac{16}{100} \cdot \frac{G M_e}{R_e^2} \]
Thus,
\[ g_p = \frac{16}{100} g_e = \frac{16}{100} \cdot \frac{G M_e}{R_e^2} \]

5. **Finding the Weight on the Hypothetical Planet:**
Now, substituting \( g_p \) back into the weight equation:
\[ W_p = m \cdot g_p = m \cdot \left(\frac{16}{100} g_e\right) \]
Since \( W_e = m \cdot g_e \), we can express \( m \) in terms of \( W_e \):
\[ m = \frac{W_e}{g_e} \]
Therefore,
\[ W_p = \frac{W_e}{g_e} \cdot \left(\frac{16}{100} g_e\right) = W_e \cdot \frac{16}{100} \]

6. **Calculating the Weight:**
Now substituting \( W_e = 600 \, \text{N} \):
\[ W_p = 600 \cdot \frac{16}{100} = 600 \cdot 0.16 = 96 \, \text{N} \]

### Final Answer:
The weight of the person on the hypothetical planet is **96 N**.