Question

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

Answer 1

Correct Answer - 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%`