The escape velocity of an object from the earth depends upon...

The escape velocity of an object from the earth depends upon the mass of earth (M), its mean density ( $p$ ), its radius (R) and gravitational constant (G), thus the formula for escape velocity is (A) $U=\mathrm{R} \sqrt{[}(8 \pi / 3) \mathrm{Gp}]$ (C) $\mathrm{U}=\sqrt{(2 \mathrm{GMR})}$ (D) $U=\sqrt{\left[(2 \mathrm{GMR}) / \mathrm{R}^{2}\right]}$

The escape velocity of an object from the earth depends upon the mass of earth (M), its mean density ( $p$ ), its radius
(R) and gravitational constant (G), thus the formula for escape velocity is
(A) $U=\mathrm{R} \sqrt{[}(8 \pi / 3) \mathrm{Gp}]$
(C) $\mathrm{U}=\sqrt{(2 \mathrm{GMR})}$
(D) $U=\sqrt{\left[(2 \mathrm{GMR}) / \mathrm{R}^{2}\right]}$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Dimensional Analysis

Dimensional analysis is a method used to verify that the units on both sides of an equation are consistent. It is a powerful tool in physics for deriving formulas, checking the correctness of derived relationships, and ensuring that equations are physically meaningful.

Escape Velocity

Escape velocity is the minimum speed that an object must reach to break free from the gravitational pull of a celestial body without further propulsion. It is derived by equating the object's kinetic energy to its gravitational potential energy and is crucial in understanding orbital mechanics and space travel.

Gravitational Constant (G)

The gravitational constant is a fundamental physical constant that appears in Newton's law of universal gravitation. It quantifies the intensity of the gravitational force between two masses and is essential in calculating gravitational forces, potential energies, and escape velocities.

Mass-Density-Radius Relationship

The mass of a spherical object, especially in astrophysical contexts, is often related to its mean density and radius by the formula M = (4/3)?R³?. This relationship is important when expressing gravitational quantities in terms of density rather than mass, and it plays a key role in deriving formulas that include escape velocity.

Transcript

Please give Ace some feedback