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) gt T_(ma)`
B. `T_(ma) gt T_(st)`
C. `T_(sp) lt T_(is)`
D. `T_(st)=T_(ma)=T_(sp)=T_(is)`

Answer

C

Explanation

(i) Time period of revolution of a satellite just about the earth’s surface
`T_(st)=2pisqrt((R+h)^3)/(GM))=2pisqrt((R^3)/(GM))=2pisqrt(R/g)`
(ii) Time period of oscillation of mass inside the tunnel bored along the diameter of the earth
`(T_(ma))`
`T_(ma)=2pisqrt(R/g)`
(iii) `T_(SP)=2pisqrt(1/(g91/l+1/R)))=2pisqrt(R/(2g)),l=R`
(iv) `T_(is)=2pisqrt(R/g),` as `ltooo`