You visited us 1 times! Enjoying our articles? Unlock Full Access!

Error and Uncertainty

A physical qu...

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:

(a x + b y - c z) %

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(a x - b y - c z) %

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(a x + b y + c z) %

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

(a x - b y + c z) %

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $(a x + b y + c z) %$
$X = [M^{x} L^{- x y} T^{- z}]$
% error in $M = a$ %
% error in $L = b$ %
% error in $T = c$ %
$\frac{Δ X}{X} \times 100 = [x \frac{Δ M}{M} + y \frac{Δ L}{L} + z \frac{Δ T}{T}] \times 100$
$= a x + b y + c z$
Maximum error in $X = (a x + b y + c z)$ %

Suggest Corrections

Similar questions

X

X = [M^{η} L^{- θ} T^{- ϕ}]

M, L

T

α

β

γ

X

x, y, z, u

x = b y + c z + d u, y = c z + d u + a x, z = d u + a x + b y, u = a x + b y + c z

f (x, y, z) = x y z (4 d - a x - b y - c z)

4 d - a x - b y - c z > 0

x = b y + c z + d u, y = c z + a x + d u, z = a x + b y + d u, u = a x + b y + c z .

\frac{a}{1 + a} + \frac{b}{1 + b} + \frac{c}{1 + c} + \frac{d}{1 + d}

\frac{x}{l (m b + n c - l a)} = \frac{y}{m (n c + l a - m b)} = \frac{z}{n (l a + m b - n c)},

\frac{l}{x (b y + c z - a x)} = \frac{m}{y (c z + a x - b y)} = \frac{n}{z (a x + b y - c z)} .

Join BYJU'S Learning Program