The toy hanging from the mirror.

A car accelerates forward at 5 m/s² on a level road (take g = 10 m/s²). A toy hanging on a string from the rear-view mirror settles at an angle to the vertical of about:

A car accelerating forward at 5 m/s², with a toy hanging on a string from the rear-view mirror; the angle of the string is marked θ.

Answer: 26.6°, leaning backward.

In the car's frame, the toy feels gravity downward and a pseudo-force ma backward. The string lines up with their resultant, the effective gravity, which tilts backward from the vertical.

\tan θ = \frac{a}{g} = \frac{5}{10} = 0.5

\Rightarrow θ \approx 26.6 °

So the toy leans backward at about 26.6°, while a helium balloon in the same car leans forward by the same angle. The value 63.4° is the angle measured from the horizontal instead of from the vertical.

Original practice question · JEE Physics Decoded

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