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Escape velocity: V(esc) = sqrt((2GM)/(...

Escape velocity:
`V_(esc) = sqrt((2GM)/(R))`
for earth : `V_(esc) = 11.2 km//s`
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 ?

Text Solution

Verified by Experts

Given : `M_(p) = 8M_(e)`
`R_(p) = 2R_(e)`
To find : `V_(e(p)) = ?`
Formula ` : V_(e) = sqrt((2GM)/(R))`
Solution :
(a) For earth
`V_(e) = sqrt((2GM_(e))/(R_(e))) = 11.2nkm//s" "……(i)`
(b) For the planet given,
`V_(c) = sqrt((2GM_(p))/(R_(p)))" "......(ii)`
`= sqrt((2G8M_(e))/(2R_(e))) " "because (M_(p) = 8M_(e), R_(p) = 2R_(e))`
` = sqrt((8)/(2)xx (2GM_(e))/(R_(e)))`
` = sqrt(4xx (2GM_(e))/(R_(e)))`
` = 2 xx sqrt((2GM_(e))/(R_(e)))" "....["form(i)"]`
` = 2 xx 11.2`
` = 22.4 km//s`
`therefore ` The escpae velocity for that planet will be `22.4 km//s`
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