Question

A U-tube containing a liquid is accelerated horizontally at a constant acceleration 8 m/s². If the horizontal separation between the vertical limbs is 20 cm, then find the difference in heights (in cm) of the liquid in the two limbs (g = 10 m/s²)

• A. 8 cm
• B. 10 cm
• C. 16 cm
• D. 20 cm

Answer 1

Answer: (C)

16 cm

Answer 2

The pressure difference due to horizontal acceleration is $\Delta P = \rho l a$. The pressure difference due to height difference is $\Delta P = \rho g h$. Equating both, we get $\rho l a = \rho g h$. So, $h = \frac{l a}{g}$. Given $l = 20 \text{ cm} = 0.2 \text{ m}$, $a = 8 \text{ m/s}^2$, $g = 10 \text{ m/s}^2$. $h = \frac{0.2 \times 8}{10} = \frac{1.6}{10} = 0.16 \text{ m}$. In cm, $h = 0.16 \times 100 = 16 \text{ cm}$.