A simple pendulum of length l₁ has periodic time 2.4 s. Another simple pendulum of length l₂ < l₁ , has periodic time 1.8 s. The periodic time of simple pendulum of length (l₁ - l₂) is nearly

Step-by-step solution

The time period of a simple pendulum is given by T = 2 l g . Squaring both sides, we get T^2 = 4 ^2 l g , which implies l = g T^2 4 ^2 . For the first pendulum, l₁ = g T₁^2 4 ^2 . For the second pendulum, l₂ = g T₂^2 4 ^2 . For the pendulum of length l₁ - l₂ , the time period T is given by: T^2 = 4 ^2 g (l₁ - l₂) = 4 ^2 g ( g T₁^2 4 ^2 - g T₂^2 4 ^2 ) = T₁^2 - T₂^2 Substituting the given values T₁ = 2.4 s and T₂ = 1.8 s: T^2 = (2.4)^2 - (1.8)^2 = 5.76 - 3.24 = 2.52 T = 2.52 1.587 s This is nearly 1.6 s. Answer: 1.6