Question

A long U tube is filled with a liquid of density ‘$\rho$ ’ such that length of the tube above liquid is ‘a’ in both arm. One side of tube (right arm) is sealed and the tube is inverted (‘$P_0$’ atmospheric pressure).

• A. Liquid will spill out the left tube if $a<\frac{P_0}{4\rho g}$
• B. Liquid will not spill out the left tube for any value of ‘a’
• C. Liquid surface in left arm will not move if $a=\frac{P_0}{2\rho g}$
• D. Liquid surface in right arm will come down

Answer 1

Answer: (A), (C)

The correct options are
A

Liquid will spill out the left tube if $a<\frac{P_0}{4\rho g}$

C

Liquid surface in left arm will not move if $a=\frac{P_0}{2\rho g}$

Let pressure of gas in right arm in inverted position be ‘P’.

$\therefore P(a+x)=P_0.a$ …(i)

$P+2x\rho g=P_0$ …(ii)

From (i) and (ii)

$x=\{\frac{P_0}{2\rho g}-a\}$