# Derive the relationship between #"g"# and #"G"#?

r is the distance between object and the center of earth

h is height of object from the surface and R is the radius of earth.

and

(When the object is near the surface of earth so we can neglect the height of object comparing with Radius of Earth)

By signing up, you agree to our Terms of Service and Privacy Policy

The relationship between "g" (acceleration due to gravity) and "G" (universal gravitational constant) is given by Newton's law of universal gravitation:

[ F = G \frac{m_1 \cdot m_2}{r^2} ]

Where:

- ( F ) is the gravitational force between two objects,
- ( G ) is the universal gravitational constant,
- ( m_1 ) and ( m_2 ) are the masses of the two objects, and
- ( r ) is the distance between the centers of the two objects.

At the surface of the Earth, ( F ) is the force experienced by an object due to gravity, which is equal to ( m \cdot g ), where ( m ) is the mass of the object and ( g ) is the acceleration due to gravity. Therefore, at the surface of the Earth:

[ m \cdot g = G \frac{m_{\text{Earth}} \cdot m_{\text{object}}}{R_{\text{Earth}}^2} ]

By rearranging this equation, we can solve for ( g ):

[ g = \frac{G \cdot m_{\text{Earth}}}{R_{\text{Earth}}^2} ]

Where:

- ( m_{\text{Earth}} ) is the mass of the Earth, and
- ( R_{\text{Earth}} ) is the radius of the Earth.

Therefore, the relationship between ( g ) and ( G ) is that ( g ) depends on ( G ) as well as the mass and radius of the Earth.

By signing up, you agree to our Terms of Service and Privacy Policy

- An object with a mass of #5 kg# is revolving around a point at a distance of #3 m#. If the object is making revolutions at a frequency of #5 Hz#, what is the centripetal force acting on the object?
- A model train with a mass of #6 kg# is moving along a track at #15 (cm)/s#. If the curvature of the track changes from a radius of #3 cm# to #15 cm#, by how much must the centripetal force applied by the tracks change?
- A model train, with a mass of #15 kg#, is moving on a circular track with a radius of #3 m#. If the train's rate of revolution changes from #7 Hz# to #3 Hz#, by how much will the centripetal force applied by the tracks change by?
- What is difference between the gravitational force and the force of gravity?
- An object with a mass of #5 kg# is revolving around a point at a distance of #3 m#. If the object is making revolutions at a frequency of #8 Hz#, what is the centripetal force acting on the object?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7