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

Options

A. `8% `
B. `10%`
C. `12%`
D. None

Answer

C

Explanation

Given : `X = (2k^(3) l^(2))/( m sqrtn)`
`therefore (Delta X)/(X) = 3 (Delta k)/(k) + 2 (Delta l)/(l) +(Delta m)/(m) + (1)/(2) (Delta n )/(n)`
Precentage error in X
`(Delta X)/(X) xx 100 = (3 (Delta k)/(k) + 2(Delta l)/(l)+ (Delta m)/(m) + (1)/(2) (Delta n)/(n)) xx 100 `
`" " = 3 xx 1 % + 2 xx 2% + 3% + (1)/(2) xx 4% `
`=" "3% + 4% + 3% + 2% = 12% `
Hence, the value of X is uncertain by 12 %.