Question

A physical quantity a is related to four other physical quantities a,b,c and d as follows a=a square b cube /c under root



d.The %errors of measurement in a b c and d are 1%,3%,2%,2%respectively what is percentage error in quantity a

Answer 1

it is given that physical quantity α is related to four other physical quantities a, b, c and d as follows , α = a²b³/c√d

so,

% error in α = 2 × % error in a + 3 × % error in b + % error in c + 1/2 × % error in d

given, % error in a = 1%

% error in b = 2%

% error in c = 3%

and % error in d = 4%

so, % error in α = 2 × 1% + 3 × 2 % + 3% + 1/2 × 4%

= (2 + 6 + 3 + 2)% = 13%

hence, % error in α is 13%