The value of universal gravitational constant ( G ) is 

  1. \(6.67 \times 10^{-11} \frac{N \times m^2}{kg^2}\)
  2. \(6.67 \times 10^{11} \frac{N \times m^2}{kg^2}\)
  3. \(6.67 \times 10^{-11} \frac{N \times kg^2}{m^2}\)
  4. \(6.67 \times 10^{11} \frac{N \times kg^2}{m^2}\)

Answer (Detailed Solution Below)

Option 1 : \(6.67 \times 10^{-11} \frac{N \times m^2}{kg^2}\)
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Detailed Solution

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CONCEPT:

  • Newton's law of gravitation: The gravitational force between two objects is directly proportional to the product of masses of the objects and inversely proportional to the distance between two mass.

i.e., \(F = \frac{{GMm}}{{{R^2}}}\)

Where G = universal gravitational constant, M = Mass of the 1st body m = Mass of the 2nd  body, and R = Distance between the bodies 

EXPLANATION:

The value of the universal gravitational constant is G = 6.67 × 10-11 N × m2/kg2

Hence option 1 is correct.

MISTAKE POINTS:

We have to see the units of the given value very carefully:

As we know, the unit of force (F) = N, r2 = m2 and mass (M) = kg

Therefore the unit of gravitational constant (G) is

\(\Rightarrow G = Nm^2{kg^{-2}}\)

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