A body is thrown with a velocity equal to n times the escape velocity `(v_(e))`. Velocity of the body at large distance away will be :-

Options

A. `v_(e)sqrt(n^(2)-1)`
B. `v_(e)sqrt(n^(2)+1)`
C. `v_(e) sqrt(1-n^(2))`
D. None of these

Answer

A

Explanation

At large distance potential energy = 0
Conserving mechanical energy at surface of earth and large distance from earth.
`(1)/(2)m(nv_(e))^(2)-(GMm)/(R )=(1)/(2)mv^(2)`
Also, `v_(e)=sqrt((2GM)/(R ))`
`rArr (2GMm)/(R ) (n^(2)-1)=mv^(2)`
`rArr v=sqrt((2Gm)/(R))(n^(2)-1)^(1//2)`
`rArr v=v_(e) sqrt(n^(2)-1)`