Match the derived quantity with the formula for its maximum fractional error. List - I List - II (P) Area of a square, side 'a' with error Δ a (1) 2 a Δ a (Q) Volume of a sphere, radius &#

Question

Match the derived quantity with the formula for its maximum fractional error.

List - I	List - II
(P) Area of a square, side 'a' with error $Δ a$	(1) $2 \frac{Δ a}{a}$
(Q) Volume of a sphere, radius 'r' with error $Δ r$	(2) $3 \frac{Δ r}{r}$
(R) Density, mass 'm' with error $Δ m$ , volume 'V' with error $Δ V$	(3) $\frac{Δ m}{m} + \frac{Δ V}{V}$
(S) Acceleration due to gravity, $g = \frac{2 L}{T ^{2}}$ , L with error $Δ L$ , T with error $Δ T$	(4) $\frac{Δ L}{L} + 2 \frac{Δ T}{T}$

TestHub · Accepted Answer

For A = a 2 , A Δ A ​ = 2 a Δ a ​ (P-1). For V = 3 4 ​ π r 3 , V Δ V ​ = 3 r Δ r ​ (Q-2). For ρ = V m ​ , ρ Δ ρ ​ = m Δ m ​ + V Δ V ​ (R-3). For g = T 2 2 L ​ , g Δ g ​ = L Δ L ​ + 2 T Δ T ​ (S-4).

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