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A pendulum having time period equal to two seconds is called a seconds pendulum. Those used in pendulum clocks are of this type Find the length of a second pendulum at a place where g = π2 ms-2.
Sol. . T = 2sec. T = 2π √(l/g) ⇒ 2 = 2π √(l/10) ⇒ l/10 = 1/π^2 ⇒ l = 1cm (∴ π^2 ≈ 10) 33. From the eqation, θ = π sin [π sec-1 t] ∴ ω = π sec-1 (comparing with the equation of SHM) ⇒ 2π/T = π ⇒ T = 2 sec. We know that T = 2π √(l/g) ⇒ 2 = 2 √(l/g) ⇒ 1 = √(l/g) ⇒ l = 1m. ∴ Length of the pendulum is 1m.
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