Answer :
Final answer:
The net gravitational force on a 60 kg object placed between a 165 kg object and a 465 kg object is zero due to equal and opposite forces. To experience a net force of zero elsewhere, it can be placed at two locations: between the masses or beyond the larger mass.
Explanation:
This question involves the use of Newton's law of gravitation. The gravitational force between two objects is given by the formula F = G * (m1*m2) / r², where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.
To solve part (a), we calculate the force between the 165 kg object and the 60 kg object, and similarly between the 465 kg object and the 60 kg object, and then subtract the two forces to find the net force. The 60kg object experiences equal but oppositely directed gravitational forces, therefore the net gravitational force is zero.
For part (b), set the gravitational force from the 165 kg object equal to the force from the 465 kg object and solve for r (distance from the 60 kg to one of the other masses). Since these forces are proportional to the inverse square of the distance, they will cancel each other out at two locations: one between the masses and one outside the larger mass.
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