waht is the escape velocity of a body from a planet whose mass is twice that of earth and radius half that of earth

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Solution

Dear Student ,
Escape velocity on earth is , $v_{e} = \sqrt{\frac{2 G M}{R_{e}}}$
Now if a planet has mass twice that of earth and radius half that of earth then ,
$e s c a p e v e l o c i t y o n t h a t p l a n e t i s, v_{p} = \sqrt{\frac{2 G \times 2 M}{\frac{R_{e}}{2}}} = \sqrt{\frac{8 G M}{R_{e}}} = 2 v_{e} S o t h e e s c a p e v e l o c i t y o n t h a t p l a n e t i s t w i c e t h a t o f o n t h e e a r t h .$

Regards

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waht is the escape velocity of a body from a planet whose mass is twice that of earth and radius half that of earth

Dear Student , Escape velocity on earth is , ve=2GMRe Now if a planet has mass twice that of earth and radius half that of earth then , escape velocity on that planet is ,vp=2G×2MRe2=8GMRe=2veSo the escape velocity on that planet is twice that of on the earth . Regards