Question

In a simple pendulum the breaking strength of the string is double the weight of through bob.the bob is released from rest when the string is horizontal the string breaks when it makes an angle thita with the vertical

Answer 1

Let the length of the string = L
mass of the bob = m
Tension in the string = T
instantaneous Linear speed of the bob = v

The vertical distance fallen by the bob = L Cosθ
=> KE of the bob = 1/2 m v² = mg L Cosθ
=>  Centripetal force = m v²/L = 2 m g cos θ

Balancing forces along the string: (when string just snaps)
T = 2 m g = mg cosθ + 2 mg cosθ 

=>   cosθ = 2/3      
=>   Angle = 48.189°

Answer 2

By law of conservation of energy loss in PE = gain in KE 

⇒mgL(1−cosθ)=1/2mv2

⇒mv'2/L=2mg(1−cosθ)

 At point of breaking 

mgcosθ=mv'2/L

∴mgcosθ=2mg(1−cosθ)

 2mg=3mgcosθ
cosθ=2/3
θ=cos−1(2/3)