The Gravitational Constant

Concept: The gravitational constant ( ) appears in Newton's Law of Universal Gravitation. We can derive its SI unit by rearranging this law. Step 1: Recall Newton's Law of Universal Gravitation The formula for the gravitational force ( ) between two masses ( and ) separated by a distance ( ) is: where is the universal gravitational constant. Step 2: Rearrange the formula to solve for G To find the units of , we first need to isolate on one side of the equation: Multiply both sides by : Now, divide both sides by : Step 3: Determine the SI units for each quantity in the rearranged formula
(Force): The SI unit is Newton (N).
(distance): The SI unit is meter (m). So, will have units of .
(mass): The SI unit is kilogram (kg).
(mass): The SI unit is kilogram (kg).
Therefore, will have units of . Step 4: Substitute the units into the expression for G This can also be written as: or Comparing this with the given options, option (4) matches our derived unit. Option (1) is incorrect because the denominator should be . Therefore, the SI unit of the gravitational constant (G) is .