Using two light cords a bob is held in equilibrium at A. The horizontal cord is cut and the bob is allowed to swing as a pendulum. Calculate the ratio of the tension in the supporting cord in position B to that in position A.

Explanation

Resolving the tension `T_A` at A into two components `T(A) cos theta` balances mg and `T_(B) sin theta` balances the force F.
`T_(A) cos theta = mg`…..(i)
At By the weight of the bob is resolved into two components. The component `mg cos theta` balances, the tension `T_(A)` The components mg sin 6 acts as the restoring force.
`T_(B)= mg cos theta`...........(ii)
`T_(B)/T_(A) = (mg cos theta)/(mg//cos theta) = cos^(2) theta`
`T_(B)/T_(A) = cos^(2) theta`