A rectangular plate $ 2 \mathrm{~m} \times 3 \mathrm{~m} $ is immersed in water in such a way that its greatest and least depth are $ 6 \mathrm{~m} $ and $ 4 \mathrm{~m} $, respectively, from the water surface. The total thrust on the plate is

Question

A rectangular plate $ 2 \mathrm{~m} \times 3 \mathrm{~m} $ is immersed in water in such a way that its greatest and least depth are $ 6 \mathrm{~m} $ and $ 4 \mathrm{~m} $, respectively, from the water surface. The total thrust on the plate is, $ 294 \times 10^{3} \mathrm{~N} $, $ 294 \mathrm{~N} $, $ 100 \times 10^{3} \mathrm{~N} $, $ 400 \times 10^{3} \mathrm{~N} $

MARKS App · Accepted Answer

Given the size of the plate = 2 m × 3 m and greatest and least depths of the plate are 6 m and 4 m . We know that area of the plate A = 2 × 3 = 6 m 2 . And the depth of center of the plate x - = 6 + 4 2 = 5 m ∴ Total thrust on the plate = ρ ω g A x = 10 3 × 9.8 × 6 × 5 = 294 × 10 3 N

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