The correct answer is: A. M-1L3T-2
The dimensional formula of a physical quantity is a set of powers of the fundamental physical quantities that are used to express the quantity. The fundamental physical quantities are mass (M), length (L), time (T), electric current (I), temperature (Î), amount of substance (n), and luminous intensity (Iv).
The dimensional formula of the universal gravitational constant G is M-1L3T-2. This means that G has the dimensions of mass to the power of minus one, length to the power of three, and time to the power of minus two.
The dimensional formula of G can be derived from the equation of universal gravitation, which states that the force of gravity between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them. The equation of universal gravitation can be written as:
F = Gm1m2/r2
where F is the force of gravity, m1 and m2 are the masses of the two objects, r is the distance between the two objects, and G is the universal gravitational constant.
The dimensional formula of force is ML/T2. The dimensional formula of mass is M. The dimensional formula of distance is L. Therefore, the dimensional formula of the universal gravitational constant G is M-1L3T-2.
Option A is the correct answer because it has the correct dimensions of mass to the power of minus one, length to the power of three, and time to the power of minus two. Option B has the wrong dimensions of mass to the power of minus one, length to the power of two, and time to the power of minus two. Option C has the wrong dimensions of mass to the power of minus two, length to the power of three, and time to the power of minus two. Option D has the wrong dimensions of mass to the power of minus two, length to the power of two, and time to the power of minus two.