Q: A simple pendulum mounted on a car. The car starts to accelerate on horizontal surface with constant acceleration a0 = 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 a0 …(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°