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

• A

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

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

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

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

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 $\theta$ with the vertical then the tangent angle is $$ \tan \theta=\frac{\mathrm{ma}}{\mathrm{mg}} \Rightarrow \theta=\tan ^{-1}\left(\frac{\mathrm{a}}{\mathrm{g}}\right) $$

Hence, the correct answer is option: 'B'.