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A dish containing soapy water rests on a table inside the dining car of a train. If the train accelerates forward with magnitude g/4, the angle that the free surface of the water makes with the horizontal is

1. Tan⁻¹(1/2)
2. Tan⁻¹(1/4)
3. Tan⁻¹(1/5)
4. Tan⁻¹(1/3)

Correct answer: Tan⁻¹(1/4)

Solution

A free liquid surface always sets itself perpendicular to the net (effective) acceleration. With horizontal acceleration a and vertical gravity g, the surface makes angle theta with the horizontal where tan(theta) = a/g.

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