A Physical quantity P is given below. P=A3B1/2/C-4D3/2 . . .

Question : A Physical quantity P is given below. 

P=A³B^1/2/C^-4D^3/2

The quantity which brings in the maximum percentage error in P is

a) A

b) B

c) C

d) D

Doubt by Ananya

Solution :

P=A³B^1/2/C^-4D^3/2

P=A³B^1/2C⁴/D^3/2

Remember : Error can't be subtracted, it is always added, this is why we have converted negative power of C into positive power by moving it from denominator to the numerator.

Now,

ΔP/P = 3ΔA/A + ΔB/2B + 4ΔC/C + 3ΔD/2D
ΔP/P = 3(ΔA/A) + 0.5(ΔB/B) + 4(ΔC/C) + 1.5(ΔD/D)
[ΔP/P]×100%= [3(ΔA/A) + 0.5(ΔB/B) + 4(ΔC/C) + 1.5(ΔD/D)]×100%

As we can see that The coefficient of ΔC/C is maximum i.e. 4
So we can say that the physical quantity C will bring maximum percentage error.

So the correct option is c) C.