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A tank has a hole at its bottom. The time needed to empty the tank from level `h_(1)` to `h_(2)` will be proportional toA. `h_(1)-h_(2)`B. `h_(1)+h_(2)`C. `sqrt(h_1)-sqrt(h_2)`D. `sqrt(h_1)+sqrt(h_2)` |
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Answer» Correct Answer - C Let =(dh)/(dt)` represent the rate of descent of water level. Let `A` and `a` represent the cross -sectional areas of the container and hole repectively Then , `-A(dh)/(dt) = asqrt(2gh)` `dt = -k(dh)/(sqrt(n)) dt` or `int_(0)^(t) dt = -kint_(h_1)^(h_2) (1)/(sqrt(h))dh` or `t=-k|(h^(1/2+1))/(-1/2+1)|_(h_(1))^(h_2)` or `t=-2k[sqrt(h_2)-sqrt(h_1)]` or `t prop (sqrt(h_(1) )-sqrt(h_2))`. |
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