Q134 / 160 · TS EAMCET 2024 (09 May Shift 2) · Physics
Water flows through a horizontal pipe of variable crosssection at the rate of $12 \pi$ litre per minute. The velocity of the water at the point where the diameter of the pipe becomes 2 cm is
- A$6 \mathrm{~ms}^{-1}$
- B$8 \mathrm{~ms}^{-1}$
- C$4 \mathrm{~ms}^{-1}$
- Correct answerD$2 \mathrm{~ms}^{-1}$
Solution
Given,
Rate of flow of water, $\mathrm{V}=12 \pi$ litre per minute
$=\frac{12 \pi \times 10^{-3}}{60} \mathrm{~m}^3 / \mathrm{s}$
Radius of pipe, $\mathrm{r}=1 \times 10^{-2} \mathrm{~m}$ From the equation of continuity $\begin{aligned} & \mathrm{V}=\mathrm{av} \\ & \Rightarrow \frac{12 \pi \times 10^{-3}}{60}=\pi\left(10^{-2}\right)^2 \times \mathrm{V} \\ & \Rightarrow 0.2 \times 10^{-3}=10^{-4} \mathrm{~V} \\ & \Rightarrow \mathrm{~V}=2 \mathrm{~m} / \mathrm{s} \end{aligned}$
Radius of pipe, $\mathrm{r}=1 \times 10^{-2} \mathrm{~m}$ From the equation of continuity $\begin{aligned} & \mathrm{V}=\mathrm{av} \\ & \Rightarrow \frac{12 \pi \times 10^{-3}}{60}=\pi\left(10^{-2}\right)^2 \times \mathrm{V} \\ & \Rightarrow 0.2 \times 10^{-3}=10^{-4} \mathrm{~V} \\ & \Rightarrow \mathrm{~V}=2 \mathrm{~m} / \mathrm{s} \end{aligned}$
Hence, the correct answer is option: 'D'.