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Assertion: An air bubble in water grows ...

Assertion: An air bubble in water grows in size when it rises from bottom to top.
Reason: On moving from bottom to top, pressure of the air bubble will decrease, volume will increase and hence, size of air bubble will rise.

A

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

B

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

C

If assertion is correct but reason is incorrect.

D

If assertion is incorrect but reason is correct.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze both the assertion and the reason provided in the statement. ### Step 1: Understanding the Assertion The assertion states that "An air bubble in water grows in size when it rises from bottom to top." This means that as the bubble moves upwards in the water, its volume increases. **Hint:** Think about the behavior of gases under pressure changes. ### Step 2: Understanding the Reason The reason given is that "On moving from bottom to top, the pressure of the air bubble will decrease, volume will increase and hence, the size of the air bubble will rise." This implies that as the bubble rises, the pressure exerted on it decreases, allowing it to expand. **Hint:** Recall how pressure affects the volume of gases according to Boyle's Law. ### Step 3: Analyzing the Pressure Change As the bubble rises, the pressure exerted on it decreases because the water pressure is higher at greater depths. According to the hydrostatic pressure formula, pressure increases with depth (P = P0 + ρgh). Therefore, as the bubble ascends, it experiences lower pressure. **Hint:** Remember that pressure decreases with an increase in height in a fluid. ### Step 4: Applying Boyle’s Law Boyle’s Law states that for a given mass of gas at constant temperature, the product of pressure and volume is constant (PV = constant). Since the number of moles of gas in the bubble remains constant and the temperature is assumed to be constant, a decrease in pressure will lead to an increase in volume. **Hint:** Consider how the relationship between pressure and volume allows for expansion. ### Step 5: Conclusion Since both the assertion and the reason are correct and the reason properly explains the assertion, we conclude that: - **Assertion:** Correct - **Reason:** Correct and provides a proper explanation. Thus, the correct answer is that both the assertion and the reason are correct, and the reason is a correct explanation of the assertion. **Final Answer:** Both assertion and reason are correct, and reason is a proper explanation of the assertion.
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