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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

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

Grade:12

2 Answers

Badiuddin askIITians.ismu Expert
148 Points
14 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
15 Points
5 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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