Question

A physical quantity A is dependent on other four physical quantities p, q, r and s as given below A = `sqrt("pq"/("r"^2"s"^3))`. The percentage error of measurement in p, q, r and s are 1%, 3%, 0.5% and 0.33% respectively, then the maximum percentage error in A is ______ %.

Options

• 1

• 2

• 3

• 4

Answer 1

A physical quantity A is dependent on other four physical quantities p, q, r and s as given below A = `sqrt("pq"/("r"^2"s"^3))`. The percentage error of measurement in p, q, r and s are 1%, 3%, 0.5% and 0.33% respectively, then the maximum percentage error in A is 4%.

Explanation:

`(Delta"A")/"A" = 1/2 ((Delta"P")/"P"+(Delta"q")/"q") + (2Delta"r")/"r"+(3Delta"S")/"S"`

= `1/2`[1% + 3%] + 2 × 0.5 + 3 × 0.33

= 2 + 1 + 1 

= 4%