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प्रश्न
Solve the problem.
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?
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उत्तर १
Escape velocity for Earth is
Mass of the planet, Mp = 8 `× ` Mass of the Earth (Me)
Radius of the planet, Rp = 2 `× `Radius of the Earth (Re)
Thus, the escape velocity of the planet is
उत्तर २
Given:
Mass of the planet, MP = 8 ME
Radius of the planet, RP = 2 RE
Escape velocity for the Earth, VescE = 11.2 km/s
Escape velocity for the planet, VescP =?
`V_("escP") = sqrt((2"GM"_"p")/("R"_"p")) `
=`sqrt((2"G"(8"M"_"E"))/(2"R"_"E"))`
`=sqrt(8/2 xx (2"GM"_"E")/("R"_"E")`
`= sqrt(8/2) xx sqrt((2"GM"_"E")/"R"_"E")`
`= sqrt(4) xx "V"_("escE")`
∵ `"V"_("escE") = sqrt((2"GM"_"E") /("R"_"E") `
`= 2 xx 11.2`
`"V"_("escP")` = 22.4 Km/s
Escape velocity for the planet = 22.4 km/s
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