Final answer:
The free-fall acceleration on planet z can be calculated as the gravitational constant multiplied by the mass of the planet divided by the square of the radius of the planet.
Step-by-step explanation:
The free-fall acceleration on planet z can be calculated using the formula:
acceleration = gravitational constant * mass of the planet / radius2
First, we need to determine the mass of planet z. The diameter of planet z is given as 1 * 104 km, which means the radius is half of that, 5 * 103 km. We can convert this to meters by multiplying by 1000, resulting in a radius of 5 * 106 m.
Using the given formula, we need to know the value of the gravitational constant, which is approximately 6.67 * 10-11 Nm2/kg2. Plugging in the values, we get:
acceleration = (6.67 * 10-11 Nm2/kg2) * (mass of planet z) / (5 * 106 m)2
If you have the mass of planet z, you can calculate the free-fall acceleration using this equation.