A simple pendulum has a period of 17.0s. When the length is shorten by 1.5m, its period is 8.5s. Calculate the original length of the pendulum
Answer Details
For a simple pendulum, the period T = 2π √ 1/g Since g, 2 and π are constant, => T ∝ √l ∴ T = K√l Let the original length = l thus for the length l, period T = 17s ∴ 17 = K√1 .................. [1] Again, for the new length [1 - 1.5] the period T = 8.5s ∴ 8.5 = k √ [1-1.5] ...............[2]
thus dividing eqn [1] by eqn[2] we have 17/8.5 = √(l/l-1.5) ∴2 = √(l/l-1.5) =>4 = (l/l-1.5) ∴l = 4[l-1.5] = 4l - 6.0 ∴4l - l = 6.0 3l = 6.0 l = 2.0m