Final answer:
The gravitational field intensity at the midpoint between two masses of 100 kg and 1000 kg separated by 1 meter is 0 N/kg. The gravitational potential at that point can be calculated using the formula V = -G(M₁)/R₁ - G(M₂)/R₂, considering both distances R₁ and R₂ as 0.5 meters.
Step-by-step explanation:
The question involves calculating the gravitational field intensity and the potential at the midpoint between two masses positioned 1 meter apart. We use Newton's law of universal gravitation and the principles of superposition to solve this.
Newton's law of universal gravitation states that the force (F) between two masses (M₁ and M₂) is given by F = G(M₁M₂)/R², where G is the gravitational constant (6.67 × 10⁻¹¹ Nm²/kg²) and R is the separation between the masses.
In this scenario, we have a mass of 100 kg and another of 1000 kg at a distance of 1 meter. Calculating the gravitational field intensity (g) at the midpoint involves finding the net gravitational field due to both masses at that point, which is the vector sum of the fields due to each mass separately. Since both fields will point towards their respective masses and with equal magnitude, they will cancel each other out, resulting in a net field intensity of 0 N/kg at the midpoint.
The gravitational potential (V) at a point is defined as the work done by an external force in bringing a unit mass from infinity to that point without acceleration. It is given by V = -G(M₁)/R₁ - G(M₂)/R₂ where R₁ and R₂ are the distances to the point from each mass. In this case, both distances are 0.5 meters. Calculating this, we get the gravitational potential at the midpoint.