Final answer:
To find the net gravitational force on the 50kg object, we apply Newton's law of universal gravitation with the masses and their distances. For net force to be zero on the 50kg object, it must be placed at a point where the gravitational pulls from the 200kg and 500kg masses are equal and opposite.
Step-by-step explanation:
To calculate the net gravitational force on a 50kg object placed midway between a 200kg and a 500kg object separated by 4m, we need to use Newton's law of universal gravitation. The formula for the gravitational force is F = G × (M₁ × M₂) / R², where G is the gravitational constant (6.67 × 10⁻¹¹ Nm²/kg²), M₁ and M₂ are the masses of the two bodies, and R is their separation. Since the 50kg object is placed midway, the distance from each of the larger masses is 2m.
For part (a), we have two individual forces acting on the 50kg object due to the 200kg and 500kg objects. According to the directions of these forces, one will be attractive towards the 200kg object, and the other towards the 500kg object. Since they are both attractive forces, and the 50kg object is equidistant from both masses, we add these forces to find the net force.
The position of the 50kg object to experience a net force of zero can be found by setting the gravitational force due to 200kg object equal to the gravitational force due to the 500kg object and solving for the distance from one of the masses, which would not be at the midpoint.