Final answer:
The gravitational force that the two masses of 10.0 kg and 1.0 kg exert on each other, located 1.0 meter apart, is 6.674 × 10⁻¹¹ Newtons. This can also be expressed as 6.7 times ten to the negative eleventh power (10⁻¹¹).
Step-by-step explanation:
To calculate the gravitational force between two masses, we use the formula F = GMm/R², where F is the gravitational force, G is the gravitational constant, M and m are the masses of the two objects, and R is the distance between their centers. For the two given masses of 10.0 kg and 1.0 kg, which are 1.0 meter apart, we can insert these values into the equation along with the gravitational constant G = 6.674 × 10⁻¹¹ N·m²/kg²:
F = (6.674 × 10⁻¹¹ N·m²/kg²) × (10.0 kg) × (1.0 kg) / (1.0 m)²
F = 6.674 × 10⁻¹¹ Newtons
The gravitational force that each mass exerts on the other is 6.674 × 10⁻¹¹ Newtons, which corresponds to 6.7 times ten to the negative eleventh power.