A string of a pendulum of length l is displaced through 90^ from its vertical and released. Then, the minimum streng th of the string needed to withstand the tension as, the pendulum passes through its mean position is

Step-by-step solution

Length of penduIum =l Centre of gravity of pendulum's string = l 2 When pendulum is displaced through 90^ and released, then according to law of conservation of energy. Gravitational potential energy = Kinetic energy aligned & & m g l 2 & = 1 2 m v^2 v^2=g l & v & = g l & aligned At the mean position, tension in the string is balanced by the weight as weIl as the centrifugal force. Hence, T=m g+ m v^2 l / 2 [ r= l 2 ] aligned & =m g+ 2 m l v^2 & =m g+ 2 m l ( g l)^2 from Eq. & =m g+ 2 m g l l =m g+2 m g=3 m g align