Question

A : The maximum possible error in a reading is taken as least count of the measuring instrument.

R : Error in a measurement cannot be greater than least count of the measuring instrument.

A. Both (A) and (R) are true and (R) is the correct explanation of (A)

B. Both (A) and (R) are true and (R) is not the correct explanation of (A)

C. (A) is true but (R) is false

D. Both (A) and (R) are false

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Answer

  1. Assertion: The maximum possible error in a reading is taken as the least count of the measuring instrument.

  2. Reason: Error in a measurement cannot be greater than the least count of the measuring instrument.

Explanation:

Assertion:The assertion is true. The maximum possible error in a reading is typically confined to the smallest division that the measuring instrument can accurately measure, known as the least count. For example, if a meter scale has the smallest division of 0.1 cm, its least count is 0.1 cm. Thus, if a reading is 5.4 cm, the error could be $ \pm 0.1 $ cm, meaning it could range from 5.3 cm to 5.5 cm.

Reason:The reason statement is false. While it might be expected that measurement errors do not surpass the least count of an instrument, human or personal errors can exceed this constraint. Personal errors occur due to mistakes made by the person taking the measurement and are not limited by the least count. For instance, if a person incorrectly reads a measurement of 54 cm as 57 cm using a meter scale with a least count of 0.1 cm, the error here is far greater than the least count (i.e., 3 cm).

Conclusion:

The assertion is true, but the reason is false. Personal errors can indeed surpass the least count of measuring instruments. Therefore, the correct answer is:

  • Option C: The assertion is true, but the reason is false.


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