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If mass of a planet is eight times the m...

If 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?

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Given : Mass of the planet `(M_1)` = 8 x Mass of the earth `(M_2)`
Radius of the planet `(R_1)` = 2 x Radius of the earth `(R_2)`
To find : Escape velocity `(v_"esc")` of the planet
Formula : `v_"esc"=sqrt((2GM)/R)`
Solution: Mass of earth = `6xx10^24` kg and Radius of the earth `=6.4xx10^6` m , G=Gravitational constant = `6.67xx10^(-11) Nm^2//kg^2`
`therefore` Mass of the planet = `8xx6xx10^24` kg
`therefore` Radius of the planet = `2xx6.4xx10^6` m
`v_"esc"=sqrt((2GM_1)/R_1)=sqrt((2xx6.67xx10^(-11)xx8xx6xx10^24)/(2xx6.4xx10^6))`
`=2xx11.18xx10^3`
`=22.4xx10^3`
=22.4 km/s
`(because sqrt((2xx6.67xx10^(-11)xx8xx6xx10^24)/(2xx6.4xx10^6))=11.18xx10^3)`
The escape velocity of the planet is 22.4 km/s
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