The escape velocity for a planet is `v_(e)`. A tunnel is dug along a diameter of the planet and a small body is dropped into it at the surface. When the body reaches the centre of the planet, its speed will be

Options

A. `v_(e)`
B. `(v_(e))/(sqrt(2))`
C. `(v_(e))/2`
D. zero

Answer

B

Explanation

`K_(A)+U_(A)=K_(B)+U_(B)`
`K_(A)+mV_(A)=K_(B)+mV_(B)`
`0+m(-(GM)/R)=1/2mv^(2)+m(-(3GM)/(2R))`
`1/2mv^(2)=1/2(GMm)/R`
`v=sqrt((GM)/R)=sqrt(1/2.(2GM)/R)=1/(sqrt(2))v_(e)`