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Two clocks are being tested against a standard clock located in a national laboratory At 12 : 00 : 00 noon by standard clock, the readins of the two clocks are
`{:("Day","Clock - I","Clock - II"),("Monday",12:00:05,10:15:06),("Tuesday",12:01:15,10:14:59),("Wednesday",11:59:08,10:15:18),("Thursday",12:01:50,10:15:07),("Thursday",12:01:50,10:15:07),("Friday",11:59:15,10:14:53),("Saturday",12:01:30,10:15:24),("Sunday",12:01:19,10:15:11):}`
From the Observations carefully read the following conclusive statements.
Statement I : Zero - error in clock II is much longer than zero - error in clock I.
Statement II : Zero - error can always be corrected by applying necessary corrective measures
Statement III : Precision of clock - I is more than precision of clock - II
Statement IV : Precision of clock - II is more than precision of clock - I
Pick up the correction option from the following.

A

Only I and II are correct

B

Only I, II, IV are correct

C

Only, I, II, III are correct

D

Only I and III are correct

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the readings of two clocks (Clock I and Clock II) against a standard clock and evaluate the given statements based on the observations. Here’s a step-by-step breakdown of the solution: ### Step 1: Understand the Readings We have the readings of Clock I and Clock II for each day of the week compared to the standard clock at 12:00:00 noon. - **Clock I Readings:** - Monday: 12:00:05 - Tuesday: 12:01:15 - Wednesday: 11:59:08 - Thursday: 12:01:50 - Friday: 11:59:15 - Saturday: 12:01:30 - Sunday: 12:01:19 - **Clock II Readings:** - Monday: 10:15:06 - Tuesday: 10:14:59 - Wednesday: 10:15:18 - Thursday: 10:15:07 - Friday: 10:14:53 - Saturday: 10:15:24 - Sunday: 10:15:11 ### Step 2: Calculate Zero Errors Zero error is the difference between the standard time (12:00:00) and the clock reading. - **Clock I Zero Errors:** - Monday: 5 seconds (12:00:05 - 12:00:00) - Tuesday: 75 seconds (12:01:15 - 12:00:00) - Wednesday: -52 seconds (11:59:08 - 12:00:00) - Thursday: 110 seconds (12:01:50 - 12:00:00) - Friday: -45 seconds (11:59:15 - 12:00:00) - Saturday: 90 seconds (12:01:30 - 12:00:00) - Sunday: 79 seconds (12:01:19 - 12:00:00) - **Clock II Zero Errors:** - Monday: -6,294 seconds (10:15:06 - 12:00:00) - Tuesday: -6,301 seconds (10:14:59 - 12:00:00) - Wednesday: -6,301 seconds (10:15:18 - 12:00:00) - Thursday: -6,302 seconds (10:15:07 - 12:00:00) - Friday: -6,307 seconds (10:14:53 - 12:00:00) - Saturday: -6,296 seconds (10:15:24 - 12:00:00) - Sunday: -6,299 seconds (10:15:11 - 12:00:00) ### Step 3: Analyze Statements 1. **Statement I:** Zero-error in Clock II is much longer than zero-error in Clock I. - **True:** Clock II has a significantly larger negative zero error compared to Clock I. 2. **Statement II:** Zero-error can always be corrected by applying necessary corrective measures. - **True:** Zero error can be corrected by adjusting the clock. 3. **Statement III:** Precision of Clock I is more than precision of Clock II. - **False:** Clock I has varying readings, while Clock II has consistent readings around 10:15. 4. **Statement IV:** Precision of Clock II is more than precision of Clock I. - **True:** Clock II has consistent readings, indicating higher precision. ### Step 4: Conclusion Based on the analysis: - Correct statements are I, II, and IV. ### Final Answer The correct option is: **1, 2, and 4 are correct**. ---
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