A simple pendulum of length l₁ has time period T₁ . Another simple pendulum of length l₂ (l₁ l₂ ) has time period T₂ . Then the time period of the pendulum of length (l₁-l₂ ) will be

Step-by-step solution

For a simple pendulum, T ₁=2 l₁ ~g and T ₂=2 l₂ ~g Now, T ₁ ^2=4 l₁ ~g and T ₂^2=4 l₂ ~g l₁= T ₁^2 ~g 4 and l₂= T ₂^2 ~g 4 l₁-l₂= ( T ₁^2- T ₂^2 ) g 4 Time period of pendulum of length (l₁-l₂ ) is, aligned & T =2 (l₁-l₂ ) g =2 ( ~T ₁^2- T ₂^2 ) g 4 ~g & ~T = T ₁^2- T ₂^2 aligned