An accurate pendulum clock is mounted on ground floor of a high building. How much time will it lose or gain in one day if its is transferred to top storey of a building which is h = 200m higher than the ground floor? Radius of earth is `6.4 xx 10^(6)`

Options

A. It will lose 6.2s
B. It will lose 2.7 s
C. It will gain 5.2 s
D. It will gain 1.6 s

Answer

B

Explanation

`T = 2pi sqrt(l/g)` or `T prop 1/sqrt(g)`
`therefore T^(.)/T = sqrt(g/g^(.))`
But `T^(.)/T - (1 + h/R)`
or `T. = T (1+ h/R)`
Since, `T. gt T`, the clock will lose the time.
`therefore DeltaT = T. - T = T(h/r)`
Time lost in t = 1 day is,
` = ((24 xx 3600)(200))/(6.4 xx 10^(6)) s = 2.7 s`