Question

A tube of uniform cross-sectional area and of length $l$ is closed at its lowest end. The tube is filled with water. The tube is found to increase by $\Delta l$ when pulled vertically downwards but length of column of water increase by $\delta l$ only, then fractional change in its diameter is:

• A. $\frac{l}{l+\Delta l}$
• B. $1-\sqrt{\frac{l}{l+\delta l}}$
• C. $\frac{\Delta l}{l}$
• D. $1+\sqrt{\frac{l}{l+\delta l}}$

Answer 1

The correct option is B $1-\sqrt{\frac{l}{l+\delta l}}$

$l\frac{\pi }{4}{d}^2=(l+\delta l)\frac{\pi }{4}{d_1}^2$;

$\frac{l}{(l+\delta l)}=\frac{{d_1}^2}{d^2}$;

$1-\frac{d_1}{d}=1-\sqrt{\frac{l}{l+\delta l}}$