Question

A 20 cm long capillary tube is dipped in water. The water rises up to 8 cm. If the entire arrangement is put in a freely falling elevator, the length of water column in the capillary tube will be
(a) 8 cm
(b) 6 cm
(c) 10 cm
(d) 20 cm

Answer 1

Correct option: (d)

$$\begin{gathered} \mathrm{Height}\mathrm{of}\mathrm{water}\mathrm{column}\mathrm{in}\mathrm{capillary}\mathrm{tube}\mathrm{is}\mathrm{given}\mathrm{by}: \\ \mathrm{h}=\frac{2\mathrm{Tcos\theta }}{\mathrm{r\rho g}} \\ \mathrm{A}\mathrm{free}\mathrm{falling}\mathrm{elevator}\mathrm{experiences}\mathrm{zero}\mathrm{gravity}. \\ \Rightarrow \mathrm{h}=\frac{2\mathrm{Tcos\theta }}{\mathrm{r\rho }0}=\infty \\ \mathrm{But},\mathrm{h}=20\mathrm{cm}\left(given\right) \\ \mathrm{Therefore},\mathrm{the}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{water}\mathrm{column}\mathrm{will}\mathrm{remain}\mathrm{at}\mathrm{a}\mathrm{maximum}\mathrm{of}20\mathrm{cm}. \end{gathered}$$