A pendulum has an angular amplitude θ . The tension in the string at extreme position is T 1 and at the bottom is T 2 . If it is known that T 2 = 2T 1 , then what is the value of cos θ ?

Step-by-step solution

T 1 = mg cos θ ..... (1) T 2 - mg = mv 2 l = m l 2 gh = 2 mg l 1 - cos θ l = 2 mg 1 - cos θ l or T 2 = mg + 2 mg 1 - cos θ ....... (2) Given T 2 = 2T 1 or mg + 2 mg 1 - cos θ = 2mg cos θ or cos θ = 3 4 = 0.75