Question
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.
BITSAT
Physics
Mechanical Properties of Fluids
2021
BITSAT 2021
BITSAT Physics Question (2021) — Solution
Options
- A. ^ 2 ~L ^ 2 2 g
- B. ^ 2 L^ 2 2 2 g
- C. 2 ^ 2 ~L ^ 2 g
- D. 2 2 ^ 2 ~L ^ 2 g
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 \(= _ 0 ^ 1 ( x d ^ 2 4 ) xdx ( x ^ 2 )= d ^ 2 4 ^ 2 1^ 2 2 \) (ii) This centripetal force required is provided by the weight of liquid of height 'H' From (i) and (ii) \( aligned & d ^ 2 4 H g = d ^ 2 4 ^ 2 1^ 2 2 \\ & H = ^ 2 l ^ 2 2 ~g aligned \)
Related: Physics — Mechanical Properties of Fluids · All PYQ Banks