A water hose 2 cm in diameter is used to fill a 20 litre bucket. If it takes 1 minute to fill the bucket, then the speed v at which the water leaves the hose is,

Given,

Volume = 20L

time = 1 minute = 60sec

diameter d = 2 cm = 0.02m

We know that

$$\begin{gathered} Area, A=\frac{{\mathrm{\pi d}}^2}{4} \\ A=\frac{\mathrm{\pi }}{4}{(0.02)}^2 \end{gathered}$$

Volume rate of flow

$\frac{\mathrm{volume}}{\mathrm{time}}=\frac{20\times {10}^{-3}}{60}=\frac{{10}^{-3}}{3}{\mathrm{m}}^3{\mathrm{s}}^{-1}$

$\mathrm{Volume} \mathrm{rate} \mathrm{of} \mathrm{flow} = \mathrm{Cross}-\mathrm{Section} \mathrm{Area} \mathrm{x} \mathrm{Velocity} \mathrm{of} \mathrm{Flow}$

$\mathrm{V} =\mathrm{Av}$

$$\begin{gathered} \mathrm{v}=\frac{\mathrm{V}}{\mathrm{A}}=\frac{{10}^{-3}}{3}\times \frac{4}{\mathrm{\pi }{(0.02)}^2} \\ \mathrm{v}=1.06{\mathrm{ms}}^{-1} \\ \mathrm{v}=106\mathrm{cm}/\mathrm{s} \end{gathered}$$

Hence the correct answer is 106 cm/s.