A tunnel is dug along a diameter of the planet. A particle is dropped into it at the surface. The particle reaches the centre of the planet with speed v. If `v_(e)` is the escape velocity from the surface fo the planet, then-

Options

A. `sqrt2v=v_(e)`
B. `v=v_(e)`
C. `v_(e)=sqrt3v`
D. `v_(e)=sqrt5v`

Explanation

`(1)/(2)mv^(2)=[-(GMm)/(R)]-[-(3GMm)/(2R)]`
or `(1)/(2)mv^(2)=(3GMm)/(2R)-(GMm)/(R)`
or `(v^(2))/(2)=(3GM)/(2R)-(GM)/(R)`
`(v^(2))/(2)=(GM)/(R)-(1)/(2)`
or `v=sqrt((GM)/(R))`
Also, `v_(e)=sqrt((2GM)/(R))=sqrt2v.`