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The universal gravitational constant numerically equals-
1. the product of the mass of two bodies separated by a unit distance
2. the force of attraction between two unit masses separated by a unit distance
3. the energy between two masses separated by some distance
4. all of the above

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Correct Answer - Option 2 : the force of attraction between two unit masses separated by a unit distance

The correct answer is option 2) i.e. the force of attraction between two unit masses separated by a unit distance

CONCEPT:

  • Law of Universal Gravitation: It states that all objects attract each other with a force that is proportional to the masses of two objects and inversely proportional to the square of the distance that separates their centres.

It is given mathematically as follows:

\(F = \frac{Gm_1m_2}{R^2}\)

Where m1 and m2 are the mass of two objects, G is the gravitational constant and R is the distance between their centres.

  • The gravitational constant G establishes a relationship between gravitational force, mass, and distance.
    • The value of G is 6.67 × 10-11 N kg-2 m2.

EXPLANATION:

  • From the law of universal gravitation\(F = \frac{Gm_1m_2}{R^2}\)
  • If we consider two unit masses separated by a distance of one unit i.e. R = 1 unit, m1 = m2 = 1 unit

\(⇒ F = \frac{G(1)(1)}{1^2}\)

⇒ F = G

  • Thus, the universal gravitational constant numerically equals the force of attraction between two unit masses separated by a unit distance.

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