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Assertion : The pressure at the bottom o...

Assertion : The pressure at the bottom of the sea is lesser than that near the surface.
Reason : The pressure exerted by a liquid depends upon the depth of the liquid and density of the liquid.

A

If both assertion and reason are true and reason is the correct explanation of assertion.

B

If both assertion and reason are true but reason is not the correct explanation of assertion.

C

If assertion is true but reason is false.

D

If assertion is false but reason is true.

Text Solution

AI Generated Solution

The correct Answer is:
### Step-by-Step Solution: 1. **Understanding the Assertion**: The assertion states that "The pressure at the bottom of the sea is lesser than that near the surface." We need to evaluate whether this statement is true or false. 2. **Analyzing Pressure in Fluids**: According to the principles of fluid mechanics, the pressure exerted by a liquid increases with depth. The formula for pressure in a liquid is given by: \[ P = P_0 + \rho g h \] where: - \( P \) is the pressure at depth, - \( P_0 \) is the atmospheric pressure at the surface, - \( \rho \) is the density of the liquid, - \( g \) is the acceleration due to gravity, - \( h \) is the depth of the liquid. 3. **Evaluating the Assertion**: As we go deeper into the sea (increasing \( h \)), the pressure \( P \) increases due to the additional weight of the water above. Therefore, the assertion that "the pressure at the bottom of the sea is lesser than that near the surface" is **false**. 4. **Understanding the Reason**: The reason states that "The pressure exerted by a liquid depends upon the depth of the liquid and density of the liquid." This statement is true because, as explained, pressure increases with depth and is also dependent on the density of the liquid. 5. **Conclusion**: Since the assertion is false and the reason is true, we can conclude that the correct option is: - **Option 4**: The assertion is false but the reason is true.

### Step-by-Step Solution: 1. **Understanding the Assertion**: The assertion states that "The pressure at the bottom of the sea is lesser than that near the surface." We need to evaluate whether this statement is true or false. 2. **Analyzing Pressure in Fluids**: According to the principles of fluid mechanics, the pressure exerted by a liquid increases with depth. The formula for pressure in a liquid is given by: \[ P = P_0 + \rho g h \] ...
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