The angular amplitude of a simple pendulum is ₀ . The maximum tension in its string will be

Step-by-step solution

The simple pendulum at angular amplitude ₀ is shown in the figure. T_ =m g+ m v^2 I (i) When, bob of pendulum comes from A to B , it covers a vertical distance h . ₀= l-h l h=I(I- ) (ii) Also during A to B , potential energy of bob converts into kinetic energy m g h= 1 2 m v^2 v= 2 g h (iii) Thus, using Eqs. (i), (ii) and (iii) we obtain T_ =m g+ 2 m g I I (1- ₀ )=m g+2 m g [1-1+ ₀ ^2 2 ] (By using binomial theorem) =m g (1+ ₀^2 )