A tuning is dug along the diameter of the earth. There is particle of mass `m` at the centre of the tunel. Find the minimum velocity given to the particle so that is just reaches to the surface of the earth. `(R =` radius of earth)

Options

A. `sqrt((GM)/(R))`
B. `sqrt((GM)/(2R))`
C. `sqrt((2GM)/(R))`
D. it will reach with the help of negligible velocity

Answer

A

Explanation

`K_(i) + U_(i) = K_(f) + U_(f)`
`:. (1)/(2) m nu^(2) - (3)/(2) (GMm)/(R ) = 0 - (GMm)/(R )`
Solving, we get `nu = sqrt((GM)/(R ))`