First slide

Accuracy; precision of instruments and errors in measurements

Question

A physical quantity X is represented by $X = (M^{x} L^{- y} T^{- z})$ . The maximum percentage errors in the measurement of M, L, and T, respectively, are a%, b% and c%. The maximum percentage error in the measurement of X will be

Moderate

A

$(a x + b y - c z) %$
B

$(a x - b y - c z) %$
C

$(a x + b y + c z) %$
D

$(a x - b y + c z) %$

Solution

$\begin{array}{l} X = M^{x} L^{- y} T^{- z} \\ ∴ \frac{Δ X}{X} \times 100 = x (\frac{Δ M}{M} \times 100) + y (\frac{Δ L}{L} \times 100) \\ + z (\frac{Δ T}{T} \times 100), (e r r o r s a r e a l w a y s a d d e d) \\ ∴ \frac{Δ X}{X} \times 100 = (a x + b y + c z) percent \end{array}$

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