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The gravitational potential is expressed as V = -GM/r. Determine the value of V0 for the specified arrangement of masses.

1. V0 = -2G [1 + 1/2 + 1/4 + 1/8 + ...]
2. V0 = -2G [1 - 1/2]
3. V0 = -4G
4. V0 = -2G [1 - 1/2]

Correct answer: V0 = -2G [1 + 1/2 + 1/4 + 1/8 + ...]

Solution

The given series is an infinite geometric progression with a common ratio of 1/2. The sum of the series is 2. Substituting this into the expression, V0 = -2G * 2 = -2G [1 + 1/2 + 1/4 + 1/8 + ...].

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