# A simple pendulum mounted on a car. The car starts to accelerate on horizontal surface …

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°

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°