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Find the fractional error in the me...

Find the fractional error in the measurement of ` x = A^mB^ n `

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Fractional error in ` x = ( Delta x ) / (x) = pm ( m (Delta A ) /( A) + n ( Delta B ) /( B )) `
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What is meant by error in measurements ? Give an example.

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Knowledge Check

  • A physical quantity Q is found to depend on observables x, y and z, obeying relation Q=(x^(3)y^(2))/(z) . The percentage error in the measurements of x, y and z are 1% , 2% and 4% respectively. What is percentage error in the quantity Q ?

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    B
    0.04
    C
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    D
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  • A physical quantity Q is found to depend on observables x, y and z, obeying relation Q=(x^(3)y^(2))/(z) .The percentage error in the measurements of x,y and z are 1%, 2% and 4% respectively. What is percentage error in the quantity Q ?

    A
    `4%`
    B
    `3%`
    C
    `11%`
    D
    `1%`

  • The density of a cube is measured by measuring mass and the length of its sides. If the maximum error in the measurement of mass and length are 3% and 2% respectively, then the maximum error in the measurement of the density of cube is :

    A
    `7%`
    B
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    C
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    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 :

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    The least count of a stop watch is 1//5 second. The time of 20 oscillations of a pendulum is measured to be 25 seconds. The minimum percentage error in the measurement of time will be :

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