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A physical quantity X is give by the rel...

A physical quantity `X `is give by the relation `X = (2h^(3)I^(2))/(2sqrt(n))` The percentage error in the meansurement of k ,I,m and n are `1% ,2%, 3%` and `4%` respectively The value of X is uncertain by

A

`10 %`

B

`12%`

C

`8%`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
b
Given relation `X = (2k^(3) t^(2))/(msqrt(n))`
`X prop k^(3) l^(2)m^(-1)n^(-1//2)`
percentage error in incasurement of X
`(Delta X)/(X) xx 100 = (3(Delta k)/(k) + 2 (Delta I)/(I) + (Delta m)/(m) +(1)/(2) (Delta m)/(n)) xx 100`
`= 3 xx 1% + 2 xx 2% + 3% + (1)/(2) xx 4%`
`= 3% + 4% + 3% + 2% = 12 %`
It means, the value of X is uncertain by `12%`
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Knowledge Check

  • A physical quantity X is given by X=(2k^(3)l^(2))/(msqrt(n)) The percentage error in the measurement of K,l,m and n are 1%,2%, 3% and 4% respectively. The value of X is uncertain by

    A
    0.08
    B
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    None of these

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    `4%`
    B
    `3%`
    C
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    D
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