Question

Water rises in a capillary tube to a height \(h\). Choose false statement regarding capillary rise from the following.

• A. On the surface of Jupiter, height will be less than \(h\)
• B. In a lift moving up with constant acceleration height is less than \(h\)
• C. On the surface of moon the height is more than \(h\)
• D. In a lift moving down with constant acceleration the height is less than \(h\)

Hint:

Capillary rise \(h \propto 1/g_{eff}\). Any factor reducing effective gravity increases capillary rise, and vice versa.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Capillary rise \(h = \dfrac{2T\cos\theta}{\rho g r}\). So \(h \propto \dfrac{1}{g}\).
Step 2: Detailed Explanation:
(A) Jupiter has higher \(g \Rightarrow h\) decreases -- TRUE
(B) Lift moving up with acceleration \(a\): effective \(g_{eff} = g + a \Rightarrow h\) decreases -- TRUE
(C) Moon has lower \(g \Rightarrow h\) increases -- TRUE
(D) Lift moving down with acceleration \(a\): effective \(g_{eff} = g - a \Rightarrow h\) increases (not decreases) -- FALSE
Step 3: Final Answer:
Statement (D) is false; in a downward accelerating lift, capillary rise increases.