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BITSAT2021PhysicsMechanical Properties of FluidsActual

A U - shaped tube contains a liquid of density rho and it is rotated about the left dotted line as shown in the figure. Find the difference in the levels of liquid column.

Options

  1. A² ~L ² 2 g
  2. B² L² 2 2 g
  3. C2 ² ~L ² g
  4. D2 2 ² ~L ² g

Correct answer

A. ² ~L ² 2 g

Step-by-step solution

Weight of liquid of height ( H = d ² 4 H g ) (i) Let us consider a mass dm situated at a distance (x ) from (A ) as shown in the figure. The centripetal force required for the mass to rotate (=( dm ) ² ) ( ) The total centripetal force required for the mass of length (L ) to rotate (= ₀¹ ( x d ² 4 ) xdx ( x ² )= d ² 4 ² 1² 2 ) (ii) This centripetal force required is provided by the weight of liquid of height 'H' From (i) and (ii) ( aligned & d ² 4 H g = d ² 4 ² 1² 2 & H = ² l ² 2 ~g aligned )

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