A vertical U-tube of uniform cross-section contains water upto a height of 30 cm. show that if the water in one limb is depressed and then released, its up and down motion in the two limbs of the tube is simple harmonic and calculate its time-period.
Text Solution
AI Generated Solution
To solve the problem, we will follow these steps:
### Step 1: Understand the system
We have a vertical U-tube filled with water up to a height of 30 cm. When water in one limb is depressed and then released, it will oscillate up and down.
### Step 2: Define the displacement
Let’s denote the displacement of the water from its equilibrium position as \( y \). When the water is depressed by \( y \) in one limb, it rises by \( y \) in the other limb. Therefore, the total change in height between the two limbs is \( 2y \).
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