Question

A pendulum clock can be approximated as a simple pendulum of length 1.03 m and keeps accurate time at a location where g = 9.82 m/s2. In a location where g = 9.77 m/s2, what must be the new length of the pendulum, such that the clock continues to keep accurate time (that is, its period remains the same)?

Answer 1

T = k sqrt L/g

sqrt(1.03/9.82) = sqrt (L/9.77)

so
L = 9.77 (1.03/9.82)