Question

If a pendulum-driven clock gains 8.30 s/day, what fractional change in pendulum length must be made for it to keep perfect time

Answer 1

T = 2 Π (L/g)^1/2 period of simple pendlim

T = K L^12 variation of period with length

dT = 1/2 K L^-1/2 dL

dT / T = 1 / ( 2 L) dL

dL / L = 2 dT / T = 2 * 8.3 / (60 * 60 * 24) = 1.92E-4

If L = 1 m then dL = .192 mm