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A uniform solid sphere of radius 4 m is centred at the origin O. Two smaller spheres, each of radius 1 m, are carved out from it — one centred at A(-2, 0, 0) and the other at B(2, 0, 0) — leaving spherical cavities. The mass of the remaining solid is 186/23 kg. The gravitational potential at the centre O of the original sphere is V0 = -G*X J/kg. Find the value of X.
- 3
- 4
- 6
- 9
Correct answer: 3
Solution
The full-sphere mass is 192/23 kg and each cavity mass is 3/23 kg. Potential at O = -3G(192/23)/(2*4) + 2*G(3/23)/2 = -72G/23 + 3G/23 = -3G, so X = 3.
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