if the formula for a physical quantity is X=a4b3/c1/3d1/2 and if the percentage error inhe measurement of a,b,c and d are 2%,3%,4%respectively. Calculate percentage error in X
Answers
formula for a physical quantity is X = a⁴b³/c⅓d½
for percentage error in X is given as
% error in X = 4 × % error in a + 3 × % error in b + 1/3 × % error in c + 1/2 × % error in d
given,
- percentage error in a = 1%
- percentage error in b = 2%
- percentage error in c = 3%
- percentage error in d = 4%
= 4 × 1% + 3 × 2% + 1/3 × 3% + 1/2 × 4%
= 4% + 6% + 1% + 2%
= 13%
Answer:
hey mate your answer is 21 %
Explanation:
the formula for a physical quantity is X = a'b4 cl/3d1/2
so, fractional error is given as
AX/X = 3 x (Aa/a) + 4 (Ab/b) + 1/3 x (Ac/c)
+ 1/2 x (Ad/d)
[ we know, % error = 100 x fractional error]
so, percentage error of X is given as; % error of X = 3% error of a + 4* % error of b + 1/3 x % error of c + 1/2 x % error of d
given, % error of a = 2% , % error of b = 3% , % = error of c = 3% and % error of d = 4% = =
so, % error of X 3 x 2 % + 4 x 3% + 1/3 x 3% + 1/2 x 4%
= 6% + 12% + 1% + 2%
= 21%