A physical quantity X is given by `X=(2k^(3)l^(2))/(msqrt(n))` . The percentage error in the measurements 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 %.