Question:
A U-tube containing liquid is accelerated horizontally with a constant acceleration \(a_0\). If the separation between the vertical limbs is \(l\), then the difference in the heights of the liquid in the two arms is:
A U-tube containing liquid is accelerated horizontally with a constant acceleration \(a_0\). If the separation between the vertical limbs is \(l\), then the difference in the heights of the liquid in the two arms is:
Show Hint
The free surface tilts at angle \(\tan\phi=a_0/g\); multiply by the limb separation \(l\).
Updated On: Jul 2, 2026
- \(\dfrac{a_0 l}{g}\)
- \(\dfrac{l}{g}\)
- \(\dfrac{gl}{a_0}\)
- \(l\)
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: In the frame of the accelerating tube, a pseudo-force acts on the liquid opposite to the acceleration. The liquid surface tilts so that it is perpendicular to the net effective gravity.
Step 2: The effective gravity has a vertical part \(g\) (downward) and a horizontal part \(a_0\) (backward). The free surface makes an angle \(\phi\) with the horizontal where \[\tan\phi=\frac{a_0}{g}.\] Step 3: The two vertical limbs are separated by horizontal distance \(l\). The height difference between the liquid levels in the two limbs is \[\Delta h=l\tan\phi=l\cdot\frac{a_0}{g}.\] Step 4: Therefore \[\Delta h=\frac{a_0 l}{g}.\] \[\boxed{\Delta h=\dfrac{a_0 l}{g}}\]
Step 2: The effective gravity has a vertical part \(g\) (downward) and a horizontal part \(a_0\) (backward). The free surface makes an angle \(\phi\) with the horizontal where \[\tan\phi=\frac{a_0}{g}.\] Step 3: The two vertical limbs are separated by horizontal distance \(l\). The height difference between the liquid levels in the two limbs is \[\Delta h=l\tan\phi=l\cdot\frac{a_0}{g}.\] Step 4: Therefore \[\Delta h=\frac{a_0 l}{g}.\] \[\boxed{\Delta h=\dfrac{a_0 l}{g}}\]
Was this answer helpful?
0
0
Top CPET Physics Questions
- The hexadecimal equivalent of a digital number \(10011101\) is:
- If the doping concentration in a Si-Zener diode is increased, the Zener breakdown voltage:
- Which one of the following is an example of doubly magic nuclei?
- Which radiation has maximum ionization power?
- For beta-minus decay, which statement is TRUE?
View More Questions
Top CPET Fluid Mechanics Questions
- Water and mercury are filled in two cylindrical vessels up to the same height. Both the vessels have a hole in the wall near the bottom. The velocity of water and mercury coming out of the holes are \(V_1\) and \(V_2\) respectively, then the relation between \(V_1\) and \(V_2\) is:
- What is the terminal velocity of a raindrop of radius \(0.01\,\text{mm}\), where the coefficient of viscosity is \(1.8\times10^{-5}\,\text{N-s/m}^2\) and its density is \(1.2\,\text{kg/m}^3\), density of water \(=1000\,\text{kg/m}^3\)? (Take \(g=10\,\text{m/s}^2\))
Top CPET Questions
- Which of the following is a key reason for choosing DRAM over SRAM for main memory?
- Which of the following components in an FPGA is responsible for implementing combinational and sequential logic?
- What is the main purpose of declaring a base class as virtual in multiple inheritance?
- What happens if a class contains at least one pure virtual function?
- What happens if a derived class defines a function with the same name as a base class function, but with a different parameter list?
View More Questions