Question

The escape velocity form the earth is 11 `kms^(-1)` the esacpe velocity from a planet having twice the radius and the same mean denisty as the earth would be
A. 5.5 `kms^(-1)`
B. `11 kms(-1)`
C. `15.5 kms^(-1)`
D. `22 kms^(-1)`

Answer 1

Correct Answer - D
Escape velocity `V_(e)=sqrt(2GM)/(R )`
(here ,d = mean denisty of earth)
now `v_(e ) prop Rsqrt(d)`
`therefore (V_(e))/(v_(p))=(R_(e))/(R_(p))sqrt((d_(e))/(d_(p))=(R_(e))/(2R_(e))sqrt(d_(e))/(d_(e))`
`v_(p)=2v_(e )=2xx11=232 kms^(-1)`