If radius of earth increased by 100% what is the escape velocity get increased

Asked by navinyankanchi1 | 8th Nov, 2019, 08:41: PM

Expert Answer:

escape velocity, v = ( 2 g R )1/2 ..........(1)
 
where g is acceleration due to gravity, R is radius of earth
 
variation of escape velocity in terms of variation of g and variation of R is given by,
 
( Δv/v ) = (1/2) [ ( Δg/g ) + ( ΔR/R ) ] ................(2)
 
acceleration due to gravity,  g = GM/R2 = ( G/R2 ) (4/3)πR3 = G (4/3)πR  ............(3)
 
where G is gravitation constant and M is mass of earth
 
Hence , from equation (3), we get,  if radius of earth increases by 100%,
acceleration due to gravity also increases by 100% .
 
i.e.,  ( Δg/g ) = ( ΔR/R ) = 1
 
hence from eqn.(2),  ( Δv/v ) = (1/2) [ 1 + 1 ] = 1
 
hence if radius of earth increases by 100 %, escape velocity also increases by 100 %

Answered by Thiyagarajan K | 8th Nov, 2019, 09:58: PM

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