First slide

Accuracy; precision of instruments and errors in measurements

Question

A quantity is represented by $M^{a} L^{b} T^{c} .$ The percentage error in measurement of M, L, and T are $α %, β % a n d γ %$ respectively. The percentage error in X would be

Moderate

A

$(α a + β b + γ c) %$
B

$(α a - β b + γ c) %$
C

$(α a - β b - γ c) \times 100 %$
D

None of these

Solution

Let $X = M^{a} L^{b} T^{c}$
$\frac{Δ X}{X} \times 100 = (\frac{a Δ M}{M} + \frac{b Δ L}{L} + \frac{c Δ T}{T}) \times 100$
$(α a + β b + γ c) %$

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