Question

The dimension of universal gravitational constant is:
A. $\left[ {{M^{ - 2}}{L^{ - 3}}{T^{ - 2}}} \right]$
B. $\left[ {{M^{ - 2}}{L^2}{T^{ - 1}}} \right]$
C. $\left[ {{M^{ - 1}}{L^3}{T^{ - 2}}} \right]$
D. $\left[ {M{L^2}{T^{ - 1}}} \right]$

Answer 1

Hint- The gravitational constant known as the universal constant of gravity or the Newtonian constant referred to as the letter G is an observable physical constant used in the measurement of gravitational effects in the universal gravitation law of Sir Isaac Newton and in the general relativity theory of Albert Einstein relativity.

Step-By-Step answer:
Newton's Law of Universal Gravitation tell us the gravitational force between two objects (like the sun and the Earth or the Earth and a satellite or the Earth and its moon) gravitational force \[G = 6.67 \times {10^{ - 11}}{m^3}k{g^{ - 1}}{s^{ - 2}}\] used in the formula,
 \[F = \dfrac{{G\left( {{M_1} \times {M_2}} \right)\;\;}}{{{R^2}}}\]
Where F is the gravitational force between two masses, G is the gravitational constant in N, m1 is the mass of the first object in kg, m2 is the mass of the second object in kg, and R is distance.
Dimensional formula
We know that the units of Force are $ML{T^{ - 2}}$
Therefore,

$ML{T^{ - 2}} = \dfrac{{G{M^2}}}{{{L^2}}} = G \times {M^2} \times {L^{ - 2}},$
Or, $G = \dfrac{{(ML{T^{ - 2}})}}{{({M^2}{L^{ - 2}})}} = {M^{ - 1}}{L^3}{T^{ - 2}}$ .

or, $G = {M^{ - 1}}{L^3}{T^{ - 2}}$

Hence, the correct answer is C.

Additional information-
Gravity is a force that tends to bring together two things. Anything that has mass has a force of gravity. Anything that has mass has a force of gravity. The gravity of the planet holds you up and causes things to fall. Gravity is the planet in the Sun's orbit and it holds the Moon and the Earth in place. The closest you are to an object, the greater its pull. Seriousness is the weight that brings you. It is the strength which draws on all your body's mass.

Note- See, you might apply this trick for any constant if you don't know about the constant dimension, no matter. Take the formula, hold the constant on one side and put all other elements on the other side, such as masses, distance etc. Now you have the formula for the constant, now use each element's dimension formula and solve M, L and T's powers. You will obtain your constant dimension form.