Gravitational force on the surface of the moon is only `1//6` as gravitational force on the earth. What is the weight in newtons of a 10kg object on the moon and on the earth?

Explanation

To solve the problem of finding the weight of a 10 kg object on the Moon and on Earth, we can follow these steps:

### Step 1: Understand the relationship between weight, mass, and gravitational acceleration.
The weight (W) of an object is given by the formula:
\[ W = m \times g \]
where:
- \( W \) is the weight in newtons (N),
- \( m \) is the mass in kilograms (kg),
- \( g \) is the acceleration due to gravity in meters per second squared (m/s²).

### Step 2: Calculate the weight of the object on Earth.
The acceleration due to gravity on Earth (\( g_E \)) is approximately \( 9.8 \, \text{m/s}^2 \).

Using the formula:
\[ W_E = m \times g_E \]
Substituting the values:
\[ W_E = 10 \, \text{kg} \times 9.8 \, \text{m/s}^2 \]
\[ W_E = 98 \, \text{N} \]

### Step 3: Calculate the acceleration due to gravity on the Moon.
According to the problem, the gravitational force on the Moon is \( \frac{1}{6} \) that of Earth. Therefore, the acceleration due to gravity on the Moon (\( g_M \)) is:
\[ g_M = \frac{1}{6} \times g_E = \frac{1}{6} \times 9.8 \, \text{m/s}^2 \]
Calculating this gives:
\[ g_M = \frac{9.8}{6} \approx 1.63 \, \text{m/s}^2 \]

### Step 4: Calculate the weight of the object on the Moon.
Using the same weight formula:
\[ W_M = m \times g_M \]
Substituting the values:
\[ W_M = 10 \, \text{kg} \times 1.63 \, \text{m/s}^2 \]
\[ W_M = 16.3 \, \text{N} \]

### Conclusion:
- The weight of the 10 kg object on Earth is **98 N**.
- The weight of the 10 kg object on the Moon is **16.3 N**.