A physical quantity C is related to four other quantities $p, q, r$ and $s$ as follows $C=\frac{pq^{2}}{r^{3}\sqrt{s}}$ 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 \_\_\_\_ \%.

JEE Main · 2025 · 03 Apr 2025 · Shift 2 · Units & Measurement

A physical quantity C is related to four other quantities

p, q, r

and

s

as follows

C = \frac{p q ^{2}}{r ^{3} s}

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 ____ %.

Answer: 15

When a quantity is a product of powers, fractional errors add in proportion to the magnitudes of the exponents. Writing

C = p q^{2} r^{- 3} s^{- 1/2}

, the maximum percentage error is

\frac{Δ C}{C} = 1 \cdot (1%) + 2 \cdot (2%) + 3 \cdot (3%) + \frac{1}{2} \cdot (2%)

. Summing the contributions

1% + 4% + 9% + 1%

, the percentage error in

C

15%

JEE Main · 2025 · 03 Apr 2025 · Shift 2 · Integer answer