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Grade 12Mechanics

A tube of length L is filled compeletly with an incompressible liquid of mass M and closed at the both ends the tube is then rotated in horizontal plane about one of its end with a uniform angular velocity W The force exerted by the liquid at the other end is

pallavi pradeep bhardwaj

16 Years agoGrade 12

2 Answers

Badiuddin askIITians.ismu Expert

16 Years ago

Dear pallavi

consider a small length dx at adistance x on the rod from the axis of rotation

mass of liquid in dx legth = dm = M/L dx

centrifugal force is acting on dm mass

dF = dm x ω²

F = ∫df =∫dm x ω²

=M/L ω²∫x dx limit 0 to L

=MLω²/2

this force is balance by normal reaction on fluid by other end

N = MLω²/2

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Praval Kumar sinha

7 Years ago

Look as all the liquid is not concentrated at one place so we can't simply write the formula for centrifugal force . Since we know that the liquid is incompressible .. so it exerts some less force than the centrifugal force acting on mass M .. and hence

consider a small length dx at adistance x on the rod from the axis of rotation

mass of liquid in dx legth = dm = M/L dx

centrifugal force is acting on dm mass

dF = dm x ω²

F = ∫df =∫dm x ω²

=M/L ω²∫x dx limit 0 to L

=MLω²/2

this force is balance by normal reaction on fluid by other end

N = MLω²/2

hence

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