Answer:
417.5 kg
Step-by-step explanation:
Since the gravitational for of attraction F, equals the weight of the object W when its close to the earth, F = GMm/R² = W = mg where m = mass of object and g = acceleration due to gravity close to the earth = 9.8 m/s².
g = GM/R² where g = acceleration due to gravity close to the earth, G = universal gravitational constant = 6.67 × 10⁻¹¹ Nm²/kg², M = mass of earth = 5.927 × 10²⁴ kg and R = radius of earth = 6.4 × 10⁶ m
So, g = GM/R²
= 6.67 × 10⁻¹¹ Nm²/kg² × 5.927 × 10²⁴ kg/(6.4 × 10⁶ m)²
= 39.53 × 10¹³ Nm²/kg ÷ 40.96 × 10¹² m²
= 9.65 N/kg
≅ 9.7 N/kg
= 9.7 m/s²
Since W = 4050 N and W = mg
m = W/g = 4050 N/9.7 m/s²
= 417.53 kg
≅ 417.5 kg
So, the mass of the object is 417.5 kg