A certain gas effuses out of two different vessels A and B.A has a circular orifice while B has a square orifice of length equal to the radius of the orifice of vessel A. The ratio of rate of diffusion of the gas from vessel A to that from vessel B is

Options

A. `pi:1`
B. `1:pi`
C. `1:1`
D. `3:2`

Explanation

To solve the problem of the ratio of the rate of diffusion of gas from vessel A (with a circular orifice) to vessel B (with a square orifice), we can follow these steps:

### Step 1: Identify the areas of the orifices
- For vessel A, the orifice is circular with a radius \( R \).
- The area \( A_A \) of the circular orifice is given by the formula:
\[ A_A = \pi R^2 \]

- For vessel B, the orifice is square with each side equal to the radius \( R \).
- The area \( A_B \) of the square orifice is given by the formula:
\[ A_B = R^2 \]

### Step 2: Write the formula for the ratio of rates of diffusion
- The rate of diffusion is proportional to the area of the orifice. Therefore, the ratio of the rates of diffusion from vessel A to vessel B can be expressed as:
\[ \text{Rate of diffusion from A} : \text{Rate of diffusion from B} = A_A : A_B \]

### Step 3: Substitute the areas into the ratio
- Substituting the areas we found:
\[ \text{Rate of diffusion from A} : \text{Rate of diffusion from B} = \pi R^2 : R^2 \]

### Step 4: Simplify the ratio
- We can simplify the ratio by dividing both sides by \( R^2 \):
\[ \text{Rate of diffusion from A} : \text{Rate of diffusion from B} = \pi : 1 \]

### Step 5: State the final answer
- Therefore, the ratio of the rate of diffusion of the gas from vessel A to that from vessel B is:
\[ \pi : 1 \]

### Final Answer:
The ratio of the rate of diffusion from vessel A to vessel B is \( \pi : 1 \).

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