The pressure at two points in a liquid in pascal are P and 2P. The piston attached to the mouth of the liquid is given a push with pressure 2 Pa. The respevtive pressures at the two points now are in the ratio

Options

A. `(P - 2)/(2P - 2)`
B. `(P + 2)/(2P + 2)`
C. `(P + 1)/(2P + 1)`
D. `(P - 1)/(2P - 1)`

Answer

To solve the problem, we need to analyze the situation step by step.

### Step 1: Understand the Initial Conditions
We have two points in a liquid where the pressures are given as:
- Pressure at point A = P
- Pressure at point B = 2P

### Step 2: Analyze the Effect of the Piston Push
The piston attached to the mouth of the liquid is pushed with a pressure of 2 Pa. This means that we need to add this pressure to the existing pressures at both points A and B.

### Step 3: Calculate the New Pressures
- The new pressure at point A after the piston is pushed:
\[ P_A' = P + 2 \text{ Pa} \]
- The new pressure at point B after the piston is pushed:
\[ P_B' = 2P + 2 \text{ Pa} \]

### Step 4: Write the Ratio of the New Pressures
Now we need to find the ratio of the new pressures at points A and B:
\[ \text{Ratio} = \frac{P_A'}{P_B'} = \frac{P + 2}{2P + 2} \]

### Step 5: Simplify the Ratio
To simplify the ratio, we can factor out the common terms:
\[ \text{Ratio} = \frac{P + 2}{2(P + 1)} \]

### Conclusion
Thus, the final ratio of the pressures at points A and B after the piston is pushed is:
\[ \text{Ratio} = \frac{P + 2}{2(P + 1)} \]