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An open rectangular tank 10 m long and 2 m deep contains oil (specific gravity 0.80) filled to a depth of 1.5 m. The tank is uniformly accelerated from rest along its length to reach a speed of 10 m/s. Find the minimum time in which this speed can be reached without any oil spilling over. [g = 10 m/s²]
- 10 s
- 15 s
- 20 s
- 25 s
Correct answer: 10 s
Solution
Under horizontal acceleration the oil surface tilts with slope tan(theta) = a/g. The surface rotates about the mid-length, so the rise at the rear wall equals (slope) times (half the tank length). The 0.5 m air gap fixes the maximum slope, hence the maximum acceleration, and minimum time = v / a_max.
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