Final answer:
The weight of an object 100 kg on the surface of the planet whose mass and diameter are 4.8 x 10²⁴ kg and 1200 km is 883 N. Thus, the result does not match any of the provided options.
Step-by-step explanation:
To calculate the weight of a 100 kg object on the surface of another planet, we must find the acceleration due to gravity on that planet and use the formula weight (w) = mass (m) × gravity (g). The acceleration due to gravity can be calculated using the formula g = (G × M) / r², where G is the gravitational constant (6.674 × 10⁻¹¹ Nm²/kg²), M is the mass of the planet, and r is the radius of the planet.
First, let's convert the diameter of the planet to its radius in meters: the diameter is 1200 km, therefore the radius is 1200 / 2 = 600 km, which is 600,000 meters. Now, we'll use the values given:
- Mass of planet M = 4.8 × 10²⁴ kg
- Radius of planet r = 600,000 m
The acceleration due to gravity on the surface of the planet is:
g = (6.674 × 10⁻¹¹ Nm²/kg²) × (4.8 × 10²⁴ kg) / (600,000 m)²
= 8.83 m/s².
The weight of the 100 kg object would be:
w = mg = (100 kg) × (8.83 m/s²) = 883 N.
However, none of the options provided in the question match this result, which suggests there might be an error in the options or in the calculations above.