Question

The value of escape velocity of a body from the earth’s surface is V_esc = ______

Options

• `sqrt((GM)/R)`

• `2sqrt((GM)/R)`

• `sqrt((2GM)/R)`

• `sqrt((GM)/2R)`

Answer 1

The value of escape velocity of a body from the earth’s surface is V_esc = `bbunderline(sqrt((2GM)/R))`

Explanation:

The escape velocity (V_esc) is the minimal velocity required to escape the Earth's gravitational attraction without further propulsion. The equation for escape velocity from the surface of the Earth (or any planet) is derived from the conservation of energy:

Kinetic energy needed to escape = Gravitational potential energy at the surface.

`1/2mV_(esc)^2 = (GMm)/R`

Where:

• m = mass of the body
• GGG = universal gravitational constant
• MMM = mass of the Earth
• RRR = radius of the Earth

Rearranging for V_esc:

`V_(esc) = sqrt((2GM)/R)`