Q: A simple pendulum mounted on a car. The car starts to accelerate on horizontal surface with constant acceleration a_{0} = g/√3 . The maximum deflection of pendulum from vertical is

(a) 30°

(b) 45°

(c) 60°

(d) 90°

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Ans: (a)

Sol: Let deflection of pendulum from vertical is θ

If T be the tension in the String

T cosθ = m g …(i)

T sinθ = m a_{0} …(ii)

On dividing (ii) by (i)

$\displaystyle tan\theta = \frac{a_0}{g} $

$\displaystyle tan\theta = \frac{g/\sqrt{3}}{g} = \frac{1}{\sqrt{3}}$

θ = 30°