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 ?

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

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PhysicsW.E.P.Vertical circular motionEasy2 minQB

PhysicsEasynumerical

A pendulum has an angular amplitude $θ$ . The tension in the string at extreme position is T₁and at the bottom is T₂. If it is known that T₂= 2T₁, then what is the value of $\cos θ$ ?

Answer:

0.75

Solution:

$T_{1} = mg cos θ$ ..... (1)

$T_{2} - mg = \frac{{mv}^{2}}{l} = \frac{m}{l} (2 gh)$

$= \frac{2 mg}{l} (1 - cos θ) l$

$= 2 mg (1 - cos θ) l$

or $T_{2} = mg + 2 mg (1 - cos θ)$ ....... (2)

Given T₂= 2T₁

or $mg + 2 mg (1 - cos θ) = 2mg cos θ$

or $cos θ = \frac{3}{4}$
= 0.75

Stream:JEESubject:PhysicsTopic:W.E.P.Subtopic:Vertical circular motion

⏱ 2mℹ️ Source: QB

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