An object of mass is projected from center of earth along a smoot tunnel dug along te horizontal diameter as shown in the figure. Then choose the conditon on values of v for the object to cross P at least twice.

Options

A. `(sqrt(gR))/(2)ltVltsqrt(gR)`
B. `(sqrt(gR))ltVltsqrt(3gR)`
C. `sqrt(gR)//2ltVltsqrt(3gR)`
D. `sqrt(gR)//4ltVltsqrt(3gR)`

Answer

C

Explanation

`(mv_(E)^(2))/(2)(-3)/(2)(GmM)/(R)=0` [for escape velocity `V_(E)]`
`V_(E)=sqrt(3gR)`
for S.H.M in tunnel `[omega=sqrt(g//R)]`
`V_(Max)=omegaA=(sqrt((g)/(R)))(R)/(2)=(sqrt(gR))/(2)`