Assume that a tunnel is dug across the earth (radius=R) passing through its centre. Find the time a particle takes to cover the length of the tunnel if (a) it is projected into the tunnel with a speed of `sqrt((gR)` (b) it is relased from a height R above the tunnel (c ) it is thrown vertically upward along the length of tunnel with a speed of `sqrt(gR).`

Options

A. `2pi sqrt((R )/(g))`
B. `pi sqrt((R )/(g))`
C. `(pi)/(2) sqrt((R )/(g))`
D. `(pi)/(sqrt(2)) sqrt((R )/(g))`

Answer

C

Explanation

`y = A sin omegat`

where `y = R, A = sqrt(2) R`
(`:'` derived form `v = omega sqrt(A^(2) -y^(2))), omega = sqrt((g)/(R ))`
`:.` phase differnec between `P & Q = (pi)/(2)` times difference between `P & Q = (T)/(4), t_(PQ) =(T)/(4) =?`