InterviewSolution
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InterviewSolution
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A tube of length L is filled completely with an incomeressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity `omega.` The force exerted by the liquid at the other end is |
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Answer» As is know, in rotational motion, angular velocity `omega` remains constant for all segments of the liquid in the tube. `:.` Force exerted by the liquid at the other end =Force required for rotational motion `F = mr omega^(2)` ….(i) Consider a small element of the liquid of length `dx` at a distance `x` from the centre, Mass of this element of the liquid `m = (M)/(L) dx , r = x` `:. dF = mr omega^(2) = ((M)/(L) dx) x omega^(2)` `F = (M)/(L) omega^(2) int_(0)^(L) x dx = (M)/(L)omega^(2) [(x^(2))/(2)]_(0)^(L)` `F = (M)/(L)omega^(2) ((L^(2))/(2)) = (1)/(2)M omega^(2)L` |
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