Escape velocity on earth is `11.2 "kms"^(-1)`what would be the escape velocity on a planet whose mass is 1000 times and radius is 10 times that of earth ?

Options

A. `112 "kms"^(-1)`
B. `11.2 "kms"^(-1)`
C. `1.12 "kms"^(-1)`
D. `3.7 "kms"^(-1)`

Answer

A

Explanation

`v_(e)=sqrt(2gR)=sqrt(2(GM)/(R^(2))).Ror v prop sqrt((M)/(R))`
Mass is 1000 times and radius is 10 times
`v'_(e)=sqrt(((1000M)G)/(100R))`
`rArr v'_(e)=10sqrt((GM)/(R))`
`rArrv'_(e)=10 V_(e)rArrv'_(e)=10xx112rArr v'_(e)=112 "kms"^(-1)`
Therefore, escape velocity will become 10 times.