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Question: A physical quantity is represented by X = M<sup>a</sup>L<sup>b</sup> T<sup>–c</sup>. If percentage e...

A physical quantity is represented by X = MaLb T–c. If percentage errors in the measurements of M, L and T are a%, b% and g% respectively, then total percentage error is–

A

(a) (aa + bb – gc)%

A

(b) (aa + bb + gc)%

A

(c) (aa – bb – gc)%

A

(d) 0%

Explanation

Solution

(b)

Sol. Δxx=a(ΔMM)+b(ΔLL)+c(ΔTT)\frac { \Delta \mathrm { x } } { \mathrm { x } } = \mathrm { a } \left( \frac { \Delta \mathrm { M } } { \mathrm { M } } \right) + \mathrm { b } \left( \frac { \Delta \mathrm { L } } { \mathrm { L } } \right) + \mathrm { c } \left( \frac { \Delta \mathrm { T } } { \mathrm { T } } \right)