Which one of the following statements is true for the relation F = Gm1m2/r² ? (All symbols have their usual meanings)
- A.The quantity G depends on the local value of g, acceleration due to gravity
- B.The quantity G is greatest at the surface of the Earth
- C.The quantity G is used only when earth is one of the two masses
- D.The quantity G is a universal constant
Correct answer
Explanation
The correct answer is D, The quantity G is a universal constant. G has the same value everywhere in the universe, for any two masses.
The relation is Newton's law of universal gravitation: every two bodies attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them. G is the constant of that proportion, about 6.67 × 10⁻¹¹ N m² kg⁻². Henry Cavendish first measured it in 1798 with a torsion balance. By contrast, g, the acceleration due to gravity, is about 9.8 m/s² at the Earth's surface and changes with height, depth, latitude and the planet.
A is wrong: G does not depend on g; rather g depends on G, through g = GM/R². B is wrong: G does not change with place, so it is not greatest at the Earth's surface; that description fits g. C is wrong: the law applies to any two masses, such as the Sun and a planet or two stones.
Exam tip: G is universal and constant, 6.67 × 10⁻¹¹ N m² kg⁻²; g varies and is about 9.8 m/s² at the surface.
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