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?

If mass of a planet is eight times the mass of the earth and its radiu

1.	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?
Answer» Solution :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