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 [Ma Lb Tc].
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]
⇒ [Ma Lb Tc] = [M-1 L3 T-2]
∴ a = -1, b = 3, c = -2
⇒ 3a + 2b - c = 3(-1) + 2(3) - (-2) = -3 + 6 + 2 = 5