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Two immiscible liquids P and Q of different densities are contained in a wide U-tube as shown in Fig. 12.54. The heights of the two liquids above the horizontal line XX' which cuts the boundary between the liquids are Hp and HQ respectively. The U-tube is transported to a planet where the acceleration of free fall is $\frac{2}{3}$ that on the earth, where the 3 liquids do not evaporate and where the heights of liquid (measured relative to XX' ) are h_p and h_Q respectively.
Which of the given statements is correct?

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Both liquid levels rise up so that h_p - h_Q = H_p -H_Q

The liquid P falls and liquid Q rises such that $\frac{h_{p}}{h_{Q}} = \frac{2 H_{p}}{3 H_{Q}}$

Both liquid levels rise up so that h_p /H_p = h_Q /H_Q

The liquid levels are unchanged, i.e., h_p = H_p and h_Q = H_Q

answer is A.

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Detailed Solution

$ρ_{1} g h_{1} = ρ_{2} g h_{2} s o l i q u i d c o l u m n h e i g h t s a r e i n d e p e n d e n t o f a c c e l e r a t i o n d u e t o g r a v i t y .$

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