In the following four periods
(i) Time of revolution of a satellite just above the earth's surface `(T_(st))`
(ii) Period of oscillation of mass inside the tunnel bored along the diameter of the earth `(T_(ma))`
(iii) Period of simple pendulam having a length equal to the earth's raduis in a unifrom field of `9.8 N//kg(T_(sp))`
(iv) Period of an infinite length simple pendulam in the earth's real gravitational field `(T_(is))`

Options

A. `T_(st)gtT_(ma)`
B. `T_(ma)gtT_(st)`
C. `T_(sp)gtT_(is)`
D. `T_(st)=T_(ma)=T_(sp)=T_(is)`

Answer

C

Explanation

(i) `T_(st)=2pisqrt(((R+h)^(3))/(GM))=2pisqrt(R/g)`
[As `hlt lt R` and `GM=gR^(2)`]
(ii) `T_(ma)=2pisqrt(R/g)`
(iii) `T_(sp)=2pisqrt(1/(g(1/l+1/R)))=2pisqrt(R/(2g))` [As `l=R`]
(iv) ` T_(is)=2pisqrt(R/g)` [As `l=oo`]