A U TUBE OF CONSTANT AREA OF CROSS SECTION A CONTAINS LIQUID OF DENSITY d . INITIALLY, THE LIQUID IN THE TWO ARMS ARE HELD WITH A LEVEL DIFFERENCE h . AFTER BEING RELEASED THE LEVEL EQUALIZE AFTER SOMETIME. THE WORK DONE BY GRAVITATIONAL FORCE ON THE LIQUID DURING THIS PROCESS IS WHAT ?

Question

Eshan · Answer

Dear student,

After the liquid in the two tubes reach equilibrium, the liquid initially at higher level decreases by height h/2, and liquid initially at lower level rises by height h/2.
Let the height of liquid in tube at lower level be $h_1$ .

Initailly the total gravitational potential energy of the sytem= $P_1=$ $(\rho A h_1)(g)(\dfrac{h_1}{2})+(\rho A (h_1+h)(g)(\dfrac{h_1+h}{2}))$

Finally the total gravitational potential energy of system = $P_2=$
$2\times (\rho A (h_1+\dfrac{h}{2}))(g)(\dfrac{h_1+\dfrac{h}{2}}{2})=2\rho Ag\dfrac{(h_1+\dfrac{h}{2})^2}{2}$
Hence work done by gravitational force=Decrease in potential energy= $\rho Ag\dfrac{h^2}{4}$

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A U TUBE OF CONSTANT AREA OF CROSS SECTION A CONTAINS LIQUID OF DENSITY d . INITIALLY, THE LIQUID IN THE TWO ARMS ARE HELD WITH A LEVEL DIFFERENCE h . AFTER BEING RELEASED THE LEVEL EQUALIZE AFTER SOMETIME. THE WORK DONE BY GRAVITATIONAL FORCE ON THE LIQUID DURING THIS PROCESS IS WHAT ?

A U TUBE OF CONSTANT AREA OF CROSS SECTION A CONTAINS LIQUID OF DENSITY d . INITIALLY, THE LIQUID IN THE TWO ARMS ARE HELD WITH A LEVEL DIFFERENCE h . AFTER BEING RELEASED THE LEVEL EQUALIZE AFTER SOMETIME. THE WORK DONE BY GRAVITATIONAL FORCE ON THE LIQUID DURING THIS PROCESS IS WHAT ?

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A U TUBE OF CONSTANT AREA OF CROSS SECTION A CONTAINS LIQUID OF DENSITY d . INITIALLY, THE LIQUID IN THE TWO ARMS ARE HELD WITH A LEVEL DIFFERENCE h . AFTER BEING RELEASED THE LEVEL EQUALIZE AFTER SOMETIME. THE WORK DONE BY GRAVITATIONAL FORCE ON THE LIQUID DURING THIS PROCESS IS WHAT ?

A U TUBE OF CONSTANT AREA OF CROSS SECTION A CONTAINS LIQUID OF DENSITY d . INITIALLY, THE LIQUID IN THE TWO ARMS ARE HELD WITH A LEVEL DIFFERENCE h . AFTER BEING RELEASED THE LEVEL EQUALIZE AFTER SOMETIME. THE WORK DONE BY GRAVITATIONAL FORCE ON THE LIQUID DURING THIS PROCESS IS WHAT ?

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