A U tube is rotated about one of its limbs with an angular velocity - Find the difference in height H of the liquid density p level- where diameter of the tubed - L-

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Standard XII

Physics

Wave Speed expression

A U tube is r...

Question

A U tube is rotated about one of its limbs with an angular velocity $σ$ . Find the difference in height H of the liquid (density p) level, where diameter of the tubed << L.

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Solution

Concept : Centripetal force in length $L$ will press the water in level $H$ upward.
for small element $d x$ .
$d f = d m v w^{2}$
$f = \int_{L}^{O} P A \times d x \times x \times w^{2}$
$= \frac{1}{2} P A w^{2} [x^{2}]_{O}^{L}$
$= \frac{1}{2} P A w^{2} L^{2}$
$f = H P g \times A$
$\frac{1}{2} P A w^{2} L^{2} = H P g \times A$
$H = \frac{w^{2} L^{2}}{2 g}$
$A =$ area of crov section
$P =$ density of lig.

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A U tube is rotated about one of its limbs with an angular velocity σ. Find the difference in height H of the liquid (density p) level, where diameter of the tubed << L.

Concept : Centripetal force in length L will press the water in level H upward.for small element dx.df=dmvw2f=∫OLPA×dx×x×w2=12PAw2[x2]LO=12PAw2L2f=HPg×A12PAw2L2=HPg×AH=w2L22gA= area of crov sectionP= density of lig.

A U tube is rotated about one of its limbs with an angular velocity $σ$ . Find the difference in height H of the liquid (density p) level, where diameter of the tubed << L.