A body starts from rest from a point distant `r_(0)` from the centre of the earth. It reaches the surface of the earth whose radius is `R`. The velocity acquired by the body is

Options

A. `2GMsqrt(1/R-1/(r_(0)))`
B. `sqrt(2GM(1/R-1/(r_(0)))`
C. `GMsqrt(1/R-1/(r_(0)))`
D. `sqrt(GM(1/R-1/(r_(0)))`

Answer

B

Explanation

`-(GMm)/(r_(0))=1/2mv^(2)-(GMm)/R`
or `1/2mv^(2)=(GMm)/R-(GMm)/(r_(0))`
or `(v^(2))/2=(GM)/R-(GM)/(r_(0))`
or `v^(2)=2GM[1/R-1/(r_(0))]`
or `v=sqrt(2GM(1/R-1/(r_(0))))`