The maximum tension in the string of a simple pendulum is 1.2 times the minimum tension. If θ0 is the angular amplitude, then the value of θ0 is :

Engineering

Physics

SHM of Simple Pendulum

Question

The maximum tension in the string of a simple pendulum is 1.2 times the minimum tension. If θ₀ is the angular amplitude, then the value of θ₀ is :

$\cos^{- 1} (\frac{15}{16})$

$\cos^{- 1} (\frac{7}{8})$

$\cos^{- 1} (\frac{3}{4})$

$\cos^{- 1} (\frac{4}{5})$

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At extreme position,    T_min. – mg cos θ₀ = 0
T_min. = mg cos θ₀
   At lowest position,  T_max. – mg = $\frac{{mv}^{2}}{ℓ}$    ... (1)
mg ℓ (1 – cos θ₀) = $\frac{1}{2}$ mv² – 0   ... (2)
from (1) & (2)
T_max. = 3mg – 2mg cos θ₀
T_max. = 1.2 T_min.
Solving, cos θ₀ = $\frac{15}{16}$