A narrow tunnel is dug across a planet diametrically and a small body is dropped from a large height, so that it falls into the tunnel. The variation of its kinetic energy `(KE)` with distance `(r)` from the centre is represented by

Options

A.
B.
C.
D.

Answer

A

Explanation

Given `v_(0)=v_(e)//2`
`((GM)/(R+h))^(1//2)=1/2((2GM)/R)^(1//2)`
on solving , `h=R`
from the law of conservation of energy,
`-(GM)/((R+h))=1/2mv^(2)-(GMm)/R`
or `1/2mv^(2)=(GMm)/R-(GMm)/(2R)=(GMm)/(2R)`
or, `v=sqrt((GM)/R)=sqrt(gR)`
`=[(10)(6.4xx10^(6))]^(1//2)=8km//s`