Question

The value of escape speed of an object on the surface of the earth is about 11.2 km/s. If the radius of the earth would be increased by eight times without any change in its mass, what would be the value of the escape speed of an object on the surface of the earth?​

Answer 1

Answer:

Escape Velocity

How did the gas giants sweep up and hold onto their gaseous atmospheres?

How does the Earth hold onto it's atmosphere?

Why doesn't the Moon have an atmosphere?

Can atmosphere's change over time?

What is a black hole?

Whereas solids are bound to a planet (or a tiny rock or asteroid) by molecular bonds, gases can only be held to a planet by gravity.

In order to know how strongly they are held, we must understand what energy is required to escape from a planet (or any object) -- and we will measure this energy in terms of velocity -- and we then must understand how fast a gas is moving under specified conditions.

Answer 2

Answer: (2$\sqrt{2}$ * 11.2) km/s

Explanation: Escape velocity is equal to $\sqrt{2gr}$, where r is radius of planet and g is the acceleration due to gravity on that planet.

New radius = 8r

Escape velocity = $\sqrt{2g(8r)}$ =$\sqrt{16gr}$

We know that $\sqrt{2gr}$= 11.2

So, $\sqrt{16gr}$= $\frac{\sqrt{16gr}*11.2 }{\sqrt{2gr} }$ = $2\sqrt{2}$ * 11.2=31.6736 km/s