If mass of the planet is `10%` less than that of the earth and radius of the planet is `20%` greater than that of the earth then the weight of `40kg` person on that planet is

Options

A. `10 kg wt`
B. `25 kg wt`
C. `40 kg wt`
D. `60 kg wt`

Explanation

To solve the problem, we need to find the weight of a 40 kg person on a planet whose mass and radius differ from those of Earth.

### Step-by-Step Solution:

1. **Identify the mass of the planet:**
- The mass of the Earth (M_E) is taken as 1 (for simplicity).
- The mass of the planet (M_P) is 10% less than that of Earth:
\[ M_P = M_E - 0.1 \times M_E = 0.9 \times M_E = 0.9 \]

2. **Identify the radius of the planet:**
- The radius of the Earth (R_E) is taken as 1 (for simplicity).
- The radius of the planet (R_P) is 20% greater than that of Earth:
\[ R_P = R_E + 0.2 \times R_E = 1 + 0.2 = 1.2 \]

3. **Calculate the gravitational acceleration on the planet (g_P):**
- The formula for gravitational acceleration is given by:
\[ g = \frac{G \cdot M}{R^2} \]
- For Earth, the gravitational acceleration (g_E) is:
\[ g_E = \frac{G \cdot M_E}{R_E^2} = G \cdot 1 = G \]
- For the planet, substituting the values of mass and radius:
\[ g_P = \frac{G \cdot M_P}{R_P^2} = \frac{G \cdot 0.9}{(1.2)^2} = \frac{G \cdot 0.9}{1.44} = \frac{0.9G}{1.44} = 0.625G \]

4. **Calculate the weight of the person on the planet:**
- The weight of the person (W_P) on the planet can be calculated using the formula:
\[ W_P = m \cdot g_P \]
- Where \( m = 40 \, \text{kg} \):
\[ W_P = 40 \cdot (0.625G) = 25G \]

5. **Calculate the weight of the person on Earth:**
- The weight of the person on Earth (W_E) is:
\[ W_E = m \cdot g_E = 40 \cdot G \]

6. **Express the weight on the planet in terms of weight on Earth:**
- To express \( W_P \) in terms of \( W_E \):
\[ W_P = \frac{25G}{40G} \cdot W_E = \frac{25}{40} W_E = 0.625 W_E \]

7. **Calculate the final weight on the planet:**
- Since \( W_E = 40G \), we can find \( W_P \):
\[ W_P = 0.625 \times 40G = 25 \, \text{kg} \cdot G \]

### Final Answer:
The weight of the 40 kg person on the planet is \( 25 \, \text{kg} \cdot G \).