The escape velocity from a spherical satellite is `v_(e)`. The escape velocity from another satellite of double the radius and half the mean density will be

Options

A. `(V_(e))/(2)`
B. `2V_(e)`
C. `sqrt2V_(2)`
D. `(V_(e))/(3)`

Answer

C

Explanation

`v_(e1)=sqrt((2GM_(1))/(R_(1)))=sqrt((2G xx(4)/(3)pi R_(1)^(3)xx d_(1))/(R_(1)))`
`therefore v_(e1)=(2sqrt(2)R_(1))/(sqrt(3))sqrt(pi G d_(1))`
`v_(e2)=(2sqrt(2)2R_(1))/(sqrt(3))xx sqrt(pi G(d_(1))/(2))`
`therefore (v_(e2))/(v_(e1))=2sqrt((d_(1))/(2d_(1)))=(2)/(sqrt(2))=sqrt(2)`
`therefore v_(e2)=sqrt(2)v_(e1)`