Given that the length of pendulum increases by 1%. Now we need to find out how many seconds will a pendulum lose or gain per day
Equation of time period of pendulum is that :
T =
2π√ =
2Ï€() where :
T is the time period , L is length of pendulum and g is constant
Differentiate this equation with respect to L :
(T) =
[2π√] =
[2Ï€()] =
2π×() =
2π××()−× =
× ()2 =
× =
=
dT =
×dL Given that the length of pendulum increases by 1%
= 1% =
= 0.01
dL = 0.01 L
∴ dT =
× 0.01 L
dT =
× =
× =
=
0.01π√ = 0.01 ×
×2π√ = 0.005 × T
Total time per day T = 24 × 60 × 60 = 86400
dT = 0.005 × 86400 = 432 s
∴ Time lost per day , dT = 432 s