If the mass of a Planet is eight times ...

If the mass of a Planet is eight times the mass of the earth and its radius is twice the radius of the earth, what will be the escape velocity for that planet ?

Text Solution

Verified by Experts

Given Mass of planet `(M_(p))` ltbrge 8M (mass of earth),
radius of planet `(R_(p))`
=2R (radius of earth )
To find : Escape velocity of planet `(v_(p))`
Formual : `v_("esc")=sqrt((2GM)/(R))`
Calculation : From formula , `v_(p)=sqrt((2Gm_(p))/(R_(p)))=sqrt((2G(8M))/(2R))`
`=sqrt((8)/(2)xx((2GM)/(R)))`
`sqrt(4xx((2GM)/(R)))`
but , `((2GM)/(R))` is the escape velocity of the earth `(v_("esc"))` .
`therefore" " v_(p)=2v_("esc")`
We know that , `v_("esc")` =11.2 km/s
`therefore" " v_(p)=2xx11.2=22.4km//s`
The escape velocity for the planet will be 22.4 km/s .

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