Question

A physical quantity Q is given by Q = A2B3/2/C4D1/2. The percentage error in A, B, C, and D are 1%, 2%, 4% , and 2% respectively. Find the percentage error in Q.

Answer 1

Answer:

The percentage error in Q is 22%

Explanation:

According to the problem the expression is given :

Q = A^2B^3/2/C^4D^1/2

Now the percentage error in A,B,C,D are given

Now ,

ΔQ/Q=  2 x ΔA/A + 3/2 ΔB/B + 4 ΔC/C + 1/2 ΔD/D

ΔQ/Q x 100 =2 x ΔA/A x 100 + 3/2 ΔB/B  x 100 + 4 ΔC/C x 100 + 1/2 ΔD/D x100

ΔQ/Q x 100=  2 x 1 + 3/2 x 3+ 4 x 4 + 1/2 x 2

ΔQ/Q x 100= 2+3+16+1

ΔQ/Q x 100= 22

Therefore the error is Q is 22 %

Answer 2

Answer: the percentage error in Q =22%

Explanation

2(%error in A)+3/2(%error in B) +4(%error in C) +1/2(%error in D)

= 2(1%)+3/2(2%)+4(4%)+1/2(2%)

= 2%+3%+16%+1% =22%