A pendulum clock, which keeps correct time at sea level, loses `15s` per day when taken to the top of a mountain. If the radius of the earth is `6400km`, the height of the mountain is

Options

A. `1.1km`
B. `2.2km`
C. `3.3km`
D. `4.4km`

Answer

A

Explanation

At height `h(h lt lt R_e)`
`g^'=g(1-(2h)/(R_e))`
`T^'/T=sqrt(g/g^')=sqrt((g)/(g(1-2h//R_e)))`
`=(1-(2h)/(R_e))^(-1//2)=1+h/R_e`
`(T^'/T-1)=h/R_e`
`(T^'/T-1)xx86400=h/R_exx86400`
`15=(h)/(6400)xx86400`
`h=1.1km`