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An ideal fluid flows through a pipe of circular cross section with diameters \( 5 \mathrm{~cm} \) and \( 10 \mathrm{~cm} \) as
shown. The ratio of velocities of fluid at \( A \) and \( B \) is
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shown. The ratio of velocities of fluid at \( A \) and \( B \) is
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The correct answer is:
1:1
An ideal fluid flow through the pipe as shown in the following figure.
Now, (Area) \( _{A} v_{A}=(\text { Area })_{B} v_{B} \)
\[
\Rightarrow \frac{v_{A}}{v_{B}}=\frac{(\text { area })_{B}}{(\text { area })_{A}}=\frac{\Pi \times 10^{2}}{\Pi \times 5^{2}}=\frac{100}{25}=\frac{4}{1}
\]
Therefore, ratio of velocities of fluid at \( A \) and \( B \) is \( 4: 1 \).
Now, (Area) \( _{A} v_{A}=(\text { Area })_{B} v_{B} \)
\[
\Rightarrow \frac{v_{A}}{v_{B}}=\frac{(\text { area })_{B}}{(\text { area })_{A}}=\frac{\Pi \times 10^{2}}{\Pi \times 5^{2}}=\frac{100}{25}=\frac{4}{1}
\]
Therefore, ratio of velocities of fluid at \( A \) and \( B \) is \( 4: 1 \).
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