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# What is the relationship between G and g in physics?

There are differences between Gravitation (G) and Gravity (g) are as follow:

Gravitation (G) | Gravity (g) |

1. Gravitation is the force of attraction acting between any two bodies of the universe. | 1. Gravity is the earth's gravitational pull on the body, lying near the surface of the earth. |

2. It requires two masses. | 2. It requires only one mass. |

3. It is a weak force. | 3. It is a strong force. |

4. G is the Universal Gravitational Constant. | 4. g is the acceleration due to gravity. |

5. The force, $F=G\frac{M1\times M2}{{R}^{2}}$ (G = gravitational constant). | 5. The force, $F=m\times g$ (g = acceleration due to gravity). |

6. The value of G remains constant everywhere. (G = 6.673×10 | 6. The value of g varies from one place to another on the Earth. |

**There is no connection between acceleration due to gravity (g) and universal gravitation constant (G), as the value of G is constant. **Also, they are not dependent on each other.

However, a formula exists to express the relation between g and G in physics.

**$g=\frac{GM}{{R}^{2}}$**

Where,

**g = **the acceleration due to the gravity of any massive body measured in** m/s ^{2}.**

**G = **the universal gravitational constant measured in **Nm ^{2}/kg^{2}.**

**R =** the radius of the massive body measured in **km.**

**M =** the mass of the massive body measured in** Kg.**

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The relationship can be derived as-

According to the universal law of gravity,

**$F=\frac{GMm}{{R}^{2}}$ ---------------> (i)**

From Newton’s second law of motion, we can write –

**$g=\frac{F}{m}$ **---------------> (ii)**
**Substituting equation** (i)** in **(ii)** we get-

**$g=\frac{GMm}{{R}^{2}m}$**

Thus, we infer the g formula in physics as -

$g=\frac{GM}{{R}^{2}}$

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