Question

Jupiter's moon Io has active volcanoes (in fact, it is the most volcanically active body in the solar system) that eject material as high as 500 km (or even higher) above the surface. Io has a mass of 8.93×1022 kg and a radius of 1821 km .

How high would this material go on earth if it were ejected with the same speed as on Io? Earth has a mass of 5.97×1024 kg and a radius of 6356 km.

The correct answer is 72.3 km. Please explain your work. Thank you~

Answer 1

It is an interesting question and it is totally practical one...so read it carefully!!.. Students get confuse when their answer didn't match with this math!!!...

Actually the volcanic explosion acts in a different way on the Jupiter's moon!!.. as Jupiter largest planet in our solar system it has a very strong gravitational attraction force. When the moon of Jupiter lo orbit Jupiter it get streched and squeezed by attraction force of Jupiter.

The volcanic activity is a result of Io being stretched and squeezed as it orbits Jupiter. Io's rock surface bulges up and down by as much as 100 meters (328 feet) during the process. This affects Io's volcanic activity in a similar way to which Earth's oceans react to the moon. Io's irregularly elliptical orbit also heightens the tidal activity.

So the main point is the material that is ejected from the volcano get extra height for the attraction force!! And we get wrong ans because we just consider the ejection velocity for the height !! So if we simply calculate by just considering only velocity we get ans 91.16 km..

But as we already know that it should be less.....the only reason we didn't consider the attraction force !!.. which also assists in gaining the height !! So the velocity will be less that we have calculated ( v ² = ( 2 g _l H _l ) )....

So the height it will obtain will also be less than 91.16 km.. here it is given 72.3 km.