Question:
Infinite number of masses, each 1kg, are placed along the x-axis at x=±1m, ±2m, ±4m, ±8m, …. The magnitude of the resultant gravitational potential at the origin is:
Infinite number of masses, each 1kg, are placed along the x-axis at x=±1m, ±2m, ±4m, ±8m, …. The magnitude of the resultant gravitational potential at the origin is:
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Use geometric series for infinite mass distributions.
Updated On: Mar 20, 2026
- \( \dfrac{G}{2} \)
- \( G \)
- \( 2G \)
- 4G
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The Correct Option is D
Solution and Explanation
Step 1: Potential due to one mass at distance r: V = -(G)/(r)
Step 2: Sum of reciprocals: (1 + (1)/(2) + (1)/(4) + ⋯ ) = 2
Step 3: Considering both sides: V = -2G × 2 = -4G
Step 4: Magnitude = 4G.
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