Question

A quantity is represented by X = $X = M^{a}L^{b}T^{c}$. The % error in measurement of M, L and T are α%, β% and γ% respectively. The % error in X would be
(a) (αa + βb + γc)%
(b) (αa - βb + γc)%
(c) (αa - βb - γc) × 100%
(d) None of these

Answer 1

Given      X  = MaLbTc

 

Percentage error in  X  =  (∆X/X)×100

=   a(∆M/M)×100   + b(∆L/L)×100 +  c(∆T/T)×100

 

But   (∆M/M)×100  =  α;  (∆L/L)×100 =  β; (∆T/T)×100  =  γ

= ( aα + bβ  +  cγ )%

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