 # 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  Badiuddin askIITians.ismu Expert
148 Points
13 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

Please feel free to post as many doubts on our discussion forum as you can.
If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly.

All the best.

Regards,

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