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An open rectangular tank measuring 3 m (width) x 2 m (length) x 2 m (depth) is half filled with water. The tank is given a horizontal acceleration of 3.27 m/s² along the direction of its width. Taking g = 9.81 m/s², choose the correct statement about the water depth at the two ends of the tank.

1. Depth of shallow end is 0.5 m
2. Depth of shallow end is zero
3. Depth of deeper end is 1 m
4. Depth of deeper end is 2 m

Correct answer: Depth of shallow end is 0.5 m

Solution

tan(theta) = a/g = 3.27/9.81 = 1/3. The surface tilts about the centre; the change in height at each end is (W/2)*tan(theta) = 1.5*(1/3) = 0.5 m. Mean depth is 1 m, so deep end = 1.5 m and shallow end = 0.5 m.

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