Question:
Ice starts freezing in a lake with water at 0°C when the atmospheric temperature is –10°C. If the time taken for 1 cm of ice to be formed is 12 min, the time taken for the thickness of the ice to change from 1 to 2 cm will be
Ice starts freezing in a lake with water at 0°C when the atmospheric temperature is –10°C. If the time taken for 1 cm of ice to be formed is 12 min, the time taken for the thickness of the ice to change from 1 to 2 cm will be
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Ice formation slows down as thickness increases because heat has to pass through thicker ice.
Updated On: Apr 23, 2026
- 12 min
- less than 12 min
- more than 12 min but less than 24 min
- more than 24 min
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept:
Rate of ice formation follows \(x^2 \propto t\), so \(t \propto x^2\).
Step 2: Detailed Explanation:
For first 1 cm: \(t_1 = k(1)^2 = k = 12\) min.
For thickness from 0 to 2 cm: \(t = k(2)^2 = 4k = 48\) min.
Time to go from 1 cm to 2 cm = \(48 - 12 = 36\) min.
Since 36 min \(>\) 24 min, the time is more than 24 min.
Step 3: Final Answer:
Thus, time is more than 24 min.
Rate of ice formation follows \(x^2 \propto t\), so \(t \propto x^2\).
Step 2: Detailed Explanation:
For first 1 cm: \(t_1 = k(1)^2 = k = 12\) min.
For thickness from 0 to 2 cm: \(t = k(2)^2 = 4k = 48\) min.
Time to go from 1 cm to 2 cm = \(48 - 12 = 36\) min.
Since 36 min \(>\) 24 min, the time is more than 24 min.
Step 3: Final Answer:
Thus, time is more than 24 min.
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