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

• Correct answer
  A

  1:1
• B

  \( 1: 4 \)
• C

  2:1
• D

  \( 1: 2 \)

Solution

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 \( 4: 1 \).

Hence, the correct answer is option: 'A'.