Question

A \(20\) cm long capillary is dipped vertically in water. Water rises to \(8\) cm. If the arrangement is put in a freely falling elevator, the length of water column in capillary tube will be

• A. \(8\ \text{cm}\)
• B. \(10\ \text{cm}\)
• C. \(4\ \text{cm}\)
• D. \(20\ \text{cm}\)

Hint:

In free fall the effective gravity is zero, so the capillary rise formula gives an infinite height and the water fills the whole tube.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
The capillary rise is \(h=\frac{2T\cos\theta}{r\rho g_{eff}}\), where \(g_{eff}\) is the effective gravity.

Step 2: Effect of Free Fall
In a freely falling lift the system is weightless, so \(g_{eff}=0\).

Step 3: Result
With \(g_{eff}=0\) the formula gives \(h\to\infty\). The water therefore rises until it fills the entire tube.

Step 4: Compare the options
The tube is 20 cm long, so the water column is 20 cm.

Final Answer:
The water column fills the whole tube, so its length is 20 cm. \[ \boxed{\text{(D) }20\ \text{cm}} \]