To determine on which planet the gravitational field strength is the largest, we need to calculate the gravitational field strength for each planet based on the given weights and masses.
The gravitational field strength [tex]\( g \)[/tex] can be calculated using the formula:
[tex]\[ g = \frac{w}{m} \][/tex]
where [tex]\( w \)[/tex] is the weight and [tex]\( m \)[/tex] is the mass.
Let's calculate the gravitational field strength for each planet:
Planet A:
- Weight [tex]\( w_A = 2.0 \, \text{N} \)[/tex]
- Mass [tex]\( m_A = 20 \, \text{kg} \)[/tex]
[tex]\[ g_A = \frac{w_A}{m_A} = \frac{2.0 \, \text{N}}{20 \, \text{kg}} = 0.1 \, \text{N/kg} \][/tex]
Planet B:
- Weight [tex]\( w_B = 4.0 \, \text{N} \)[/tex]
- Mass [tex]\( m_B = 30 \, \text{kg} \)[/tex]
[tex]\[ g_B = \frac{w_B}{m_B} = \frac{4.0 \, \text{N}}{30 \, \text{kg}} = 0.1333 \, \text{N/kg} \][/tex]
Planet C:
- Weight [tex]\( w_C = 6.0 \, \text{N} \)[/tex]
- Mass [tex]\( m_C = 40 \, \text{kg} \)[/tex]
[tex]\[ g_C = \frac{w_C}{m_C} = \frac{6.0 \, \text{N}}{40 \, \text{kg}} = 0.15 \, \text{N/kg} \][/tex]
Planet D:
- Weight [tex]\( w_D = 8.0 \, \text{N} \)[/tex]
- Mass [tex]\( m_D = 50 \, \text{kg} \)[/tex]
[tex]\[ g_D = \frac{w_D}{m_D} = \frac{8.0 \, \text{N}}{50 \, \text{kg}} = 0.16 \, \text{N/kg} \][/tex]
Now that we have the gravitational field strength for each planet, we compare them:
- [tex]\( g_A = 0.1 \, \text{N/kg} \)[/tex]
- [tex]\( g_B = 0.1333 \, \text{N/kg} \)[/tex]
- [tex]\( g_C = 0.15 \, \text{N/kg} \)[/tex]
- [tex]\( g_D = 0.16 \, \text{N/kg} \)[/tex]
The largest gravitational field strength is [tex]\( g_D = 0.16 \, \text{N/kg} \)[/tex], which is on Planet D. Therefore, Planet D has the largest gravitational field strength.
