Which one of the following statements is true for the relation $F = \frac{Gm_1m_2}{r^2}$ ? (All symbols have their usual meanings)
The quantity G depends on the local value of g, acceleration due to gravity
The quantity G is greatest at the surface of the Earth
The quantity G is used only when earth is one of the two masses
The quantity G is a universal constant
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC NDA-1 – 2017
Let’s examine the options:
A) The quantity G depends on the local value of g, acceleration due to gravity: Incorrect. ‘g’ varies from place to place (e.g., poles vs. equator, altitude), while G is constant everywhere in the universe. ‘g’ on Earth’s surface is given by $g = \frac{GM_{Earth}}{R_{Earth}^2}$, showing that ‘g’ depends on G, not the other way around.
B) The quantity G is greatest at the surface of the Earth: Incorrect. G is a constant and does not vary with location. It has the same value on the surface of the Earth, in space, on the Moon, etc.
C) The quantity G is used only when earth is one of the two masses: Incorrect. G is used in the formula to calculate the gravitational force between *any* two masses in the universe, whether they are planets, stars, or small objects.
D) The quantity G is a universal constant: Correct. The value of G has been measured experimentally and is found to be constant throughout the universe, regardless of the nature of the masses, their distance, or the surrounding medium. Its approximate value is $6.674 \times 10^{-11} \, N m^2/kg^2$.