Certainly! Let's analyze and solve this problem step-by-step.
Step 1: Understanding the given data and the relationship between mass, weight, and gravitational acceleration.
- The mass of the body on Earth: [tex]\( m_{\text{earth}} = 2\ \text{kg} \)[/tex]
- The weight of the body on Earth: [tex]\( W_{\text{earth}} = 80\ \text{N} \)[/tex]
We also know that the weight of an object is given by the formula:
[tex]\[ W = m \cdot g \][/tex]
where:
- [tex]\( W \)[/tex] is the weight,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( g \)[/tex] is the gravitational acceleration.
Step 2: Finding the gravitational acceleration on Earth.
Given the weight [tex]\( W_{\text{earth}} \)[/tex] and mass [tex]\( m_{\text{earth}} \)[/tex], we can find the gravitational acceleration on Earth [tex]\( g_{\text{earth}} \)[/tex]:
[tex]\[ g_{\text{earth}} = \frac{W_{\text{earth}}}{m_{\text{earth}}} = \frac{80\ \text{N}}{2\ \text{kg}} = 40\ \text{m/s}^2 \][/tex]
Step 3: Determining the gravitational acceleration at another place.
We are told that the gravitational pull at the other place is one-eighth of that on Earth. Therefore, the gravitational acceleration at the other place [tex]\( g_{\text{other}} \)[/tex] is:
[tex]\[ g_{\text{other}} = \frac{g_{\text{earth}}}{8} = \frac{40\ \text{m/s}^2}{8} = 5\ \text{m/s}^2 \][/tex]
Step 4: Understanding the mass at the other place.
The mass of an object remains constant irrespective of its location. So, the mass at the other place [tex]\( m_{\text{other}} \)[/tex] is the same as the mass on Earth:
[tex]\[ m_{\text{other}} = m_{\text{earth}} = 2\ \text{kg} \][/tex]
Step 5: Calculating the weight at the other place.
Using the weight formula again at the other place:
[tex]\[ W_{\text{other}} = m_{\text{other}} \cdot g_{\text{other}} = 2\ \text{kg} \cdot 5\ \text{m/s}^2 = 10\ \text{N} \][/tex]
Conclusion:
The mass of the body at the place where the gravitational pull is one-eighth that of Earth is [tex]\( 2 \ \text{kg} \)[/tex], and its weight at that place is [tex]\( 10 \ \text{N} \)[/tex].
