A truck is stationary and has a bob suspended by a light string, in a frame attached to the truck. The truck, suddenly moves to the right with an acceleration of a. The pendulum will tilt

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to the left and the angle of inclination of the pendulum with the vertical is $\sin^{- 1} (\frac{g}{a})$

to the left and angle of inclination of the pendulum with the vertical is $\tan^{- 1} (\frac{a}{g})$

to the left and angle of inclination of the pendulum with the vertical is $\sin^{- 1} (\frac{a}{g})$

to the left and angle of inclination of the pendulum with the vertical is $\tan^{- 1} (\frac{g}{a})$

answer is B.

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Detailed Solution

As the truck move to the right, so the bob will move to the left due to inertia of rest with acceleration a
Thus, the given situation can be drawn as
From the above diagram (b) as the string moves by an angle of with the vertical then the tangent angle is
$\tan θ = \frac{ma}{mg} \Rightarrow θ = \tan^{- 1} (\frac{a}{g})$