A wire has mass (0.3 ± 0.003) gram, radius (0.5 ± 0.005) mm and length (6 ± 0.06) cm. The maximum error in the measurement of density is (a) 4% (b) 3% (c) 2% (d) 5%

Answer: (a). ρ = mπ r² l ⇒ (Δρ)/(ρ) = (Δ m)/(m) + 2(Δ r)/(r) + (Δ l)/(l) Each fractional error is 1% (units of r do not matter for a ratio): 1% + 2% + 1% So the answer is (a) 4%.

A wire has mass (0.3 ± 0.003) gram, radius (0.5 ± 0.005) mm and… | MHT CET 2026 (15 Apr, Shift 2)

Q15MHT CET 2026 · 15 APR · SHIFT 2Easy

Errors in Measurement

A wire has mass $(0.3 \pm 0.003)$ gram, radius $(0.5 \pm 0.005)$ mm and length $(6 \pm 0.06)$ cm. The maximum error in the measurement of density is

Show answer and solution

Answer: (a)

$\rho = \frac{m}{\pi r^{2} l} \Rightarrow \frac{\Delta\rho}{\rho} = \frac{\Delta m}{m} + 2\frac{\Delta r}{r} + \frac{\Delta l}{l}$
Each fractional error is $1\%$ (units of $r$ do not matter for a ratio): $1\% + 2\% + 1\%$
So the answer is (a) $4\%$ .

Report a mistake

More questions on Errors in Measurement

A quantity P is related as X⁻²Y-3/2Z2/5 where X,Y,Z are independent parameters which have…MHT CET 2026 (11 Apr, Shift 2)
The percentage error in the calculated volume of a sphere, if there is 2% error in its…JEE Main 2026 (6 Apr, Shift 2)
In an experiment the values of two spring constants were measured as k₁ = (10 ± 0.2) N/m…JEE Main 2026 (21 Jan, Shift 1)
A physical quantity C is related to four other quantities P, Q, R and S as C =…MHT CET 2026 (15 May, Shift 2)
The period of oscillation of a simple pendulum is T = 2π√(l/g) where l is about 100 cm…MHT CET 2026 (14 May, Shift 2)
A particular physical quantity is given by X = 2π√(a/b) and the measured value of 'a' is…MHT CET 2026 (12 May, Shift 1)
The percentage error in the measurement of mass of a body and its speed are 0.73% and…MHT CET 2026 (20 Apr, Shift 1)
A cuboid has volume V = l × l × √(l), where l is the length of one side. When the length…MHT CET 2026 (19 Apr, Shift 2)

Errors in Measurement question from MHT CET 2026 (15 Apr, Shift 2)

More questions on Errors in Measurement