A pendulum clock is taken `1km` inside the earth from mean sea level. Then the pendulum clock

Options

A. loses `13.5s` per day
B. gains `13.5s` per day
C. loses `7s` per day
D. gains `7s` per day

Answer

C

Explanation

`T=2pisqrt(L/g)`
`T^'=2pisqrt(L/g^')`, `g^' lt g`, `T^' gt T`, i.e., loss of time
`T^'/T=sqrt(g/g^')=sqrt((g)/(g(1-h//R_e)))=(1-h/R_e)^(-1//2)`
`=1+(h)/(2R_e)=1+(1)/(2xx6400)`
`(T^'/T-1)=(1)/(2xx6400)`
Loss of time/day `=(1)/(2xx6400)xx86400=6*75s~~7s`