Question

The CGS unit of Universal Gravitational constant is ____________
1. Dyne Cm ² g ^-2
2. Dyne ^-1Cm ² g -2
3. Dyne ^-1 Cm 2 g -2
4. Dyne  Cm 2 g -3

Answer 1

Correct Answer - Option 1 : Dyne Cm ² g ^-2

Concept:

• Newton's law of gravitation: The gravitational force between two objects is directly proportional to the product of masses of the objects and inversely proportional to the distance between two mass.

i.e., \(F = \frac{{GMm}}{{{R^2}}}\)

whereas according to classical mechanics force acting on the particle is given as

Force (F) = mass (m) × acceleration (a)

Where, F = gravitational force, M = mass of a heavier object, m = mass of a lighter object, R = distance between two masses

Cgs Unit

• The unit system of measurement where distance is measured in centimeter, weight in gram and time in second is called Cgs unit. 
• Dyne is the cgs unit of force. 

Explanation:

Now using the above equation, we can say that \(G = \frac{{F{R^2}}}{{Mm}}\)

The SI unit of force is the Newton (N).

The SI unit of distance (R) is meter (m) and the SI unit of mass is kg.

The SI unit of G = N m2/kg2 

Expressing this in cgs unit

Dyne Cm ² / gram ² =  Dyne Cm 2 g -2