Two water pipes of diameters 2 cm and 4 cm are connected with the… - Vidyadip

MCQ

Two water pipes of diameters $2\ cm$ and $4\ cm$ are connected with the main supply line. The velocity of flow of water in the pipe of $2\ cm$ diameter is:

✓
$4$ times that in the other pipe.
B
$\frac14$ times that in the other pipe.
C
$2$ times that in the other pipe.
D
$\frac12$ times that in the other pipe.

✓

Answer

Correct option: A.

$4$ times that in the other pipe.

From equation of continuity, $av =$ constant
$d_A = 2\ cm$ and $d_B = 4\ cm$
$\therefore\text{r}_\text{A}=1\text{cm}$ and $\text{r}_\text{B}=2\text{cm}$
$\therefore\frac{\text{v}_\text{A}}{\text{v}_\text{B}}=\frac{\text{a}_\text{B}}{\text{a}_\text{A}}=\frac{\pi(\text{r}_\text{B})^2}{\pi\text{(r}_\text{A})^2}$
$=\Big(\frac21\Big)^2$
$\Rightarrow\text{v}-\text{A}=4\text{v}_\text{B}$

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