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If the dimensional formula of universal gravitational constant is denoted by [MLTc], then the value of 3a + 2b - c is-
1. 1
2. -2
3. 5
4. -3

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Correct Answer - Option 3 : 5

The correct answer is option 3) i.e. 5

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.


CALCULATION:

  • Let the dimensions of gravitational constant G be [MLTc].

From the universal law of gravitation

\(⇒ G= \frac{FR^2}{m_1m_2}\)

Force (F) = mass × acceleration.

Thus, dimensions of force F = [M1 L1 T-2]

  • The dimensions of R2 = [L2]
  • The dimension of m1m2 = [M2]


\(⇒ G =\frac{[M^1 L^1 T^{-2}][L^2]}{[M^2]} \)

⇒ G = [M-1 L3 T-2]

⇒ [MLTc] = [M-1 L3 T-2]

∴ a = -1, b = 3, c = -2

⇒ 3a + 2b - c = 3(-1) + 2(3) - (-2) = -3 + 6 + 2 = 5

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