Two mass `m_(1)&m_(2)` are initially placed at rest inside two smooth tunnels in earth as shown in the figure. The minimum distance between the tunnels and the center of earth R/2 as shown in the figure. Then

Options

A. `m_(1)` will remain at rest ad `m_(2)` will perform SHM with `T.P_(2)=2pisqrt((R)/(2g))`
B. `m_(1)` will remain at rest and `m_(2)` will perform SHM wit `T.P_(2)=2pisqrt((R)/(g))`
C. `m_(1)&m_(2)` both will perform S.H.M withh same time period of `2pisqrt((R)/(g))`
D. `m_(1)` will remain at rest ad `m_(2)` will move down to other side of tunnel then move outside the earth tunnel.

Answer

C

Explanation

`F_("net"//c)=(-GmM^(1))/(r^(2))costheta`
`ma=-(GmM)/((4piR^(3))/(3))(4pi)/(4).(r^(3)x)/(r^(2)r)`
`a=-(GmM)/(mR^(3))x` or `omega=sqrt((GM)/(R^(3)))=sqrt((g)/(R))`
`therefore` T.P. in any earth tunnel is `T=2pisqrt(R//g)`