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Physics Question 46 – JEE-MAIN 2025

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A physical quantity C is related to four other quantities p, q, r and s as follows C=pq2r3s The percentage errors in the measurement of p, q, r and s are 1%, 2%, 3% and 2%, respectively. The percentage error in the measurement of C will be _______.\%

When quantities are multiplied or divided, their relative errors add up.

Step 1: Identify the relationship and error propagation rule✦ Active

The given relationship is C=pq2r3s. This can be written as C=p1q2r−3s−1/2. For a quantity X=AaBbCc, the maximum percentage error is given by:

ΔCC×100%=(|1|Δpp+|2|Δqq+|−3|Δrr+|−12|Δss)×100%

Since errors always add up, we take the absolute values of the powers.

Step 2: Substitute the given percentage errors○ Expand

The percentage errors are given as: Δpp×100%=1%, Δqq×100%=2%, Δrr×100%=3%, and Δss×100%=2%. Substitute these values into the error propagation formula:

ΔCC×100%=(1(1%)+2(2%)+3(3%)+12(2%))
💡 Teacher's Secret Hint

Remember to use the absolute values of the powers for error propagation.

Step 3: Calculate the total percentage error○ Expand

Perform the summation:

ΔCC×100%=(1%+4%+9%+1%)=15%

Thus, the percentage error in the measurement of C is 15%.

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