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Three identical uniform spheres, each of mass M and radius R, are arranged so that every sphere touches the other two. Find the magnitude of the net gravitational force on any one sphere due to the other two.
- G*M²/(4R²)
- 2*G*M²/R²
- 2*G*M²/(4R²)
- sqrt(3)*G*M²/(4R²)
Correct answer: sqrt(3)*G*M²/(4R²)
Solution
Centre separation = 2R. Force between a pair: F = G*M²/(2R)² = G*M²/(4R²). On one sphere, two equal forces of magnitude F act with 60 deg between them. Resultant = 2*F*cos(30 deg) = 2*F*(sqrt(3)/2) = sqrt(3)*F = sqrt(3)*G*M²/(4R²).
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