Question

The mass of the wire of radius r and length L is measured to be M=0.3+-0.003.If r=0.5+-0.006mm and L=6+-0.06cm.The maximum percentage error in density

Answer 1

Answer:

4%

Explanation:

The volume of the wire is given by, V=πr

2

L

Thus density of the wire, ρ=

πr

2

L

m

Taking log and then differentiate:

⟹

ρ

Δρ

×100=

m

Δm

×100+2

r

Δr

×100+

L

ΔL

×100

∴

ρ

Δρ

×100=

0.3

0.003

×100+2

0.5

0.005

×100+

6

0.06

×100=4%.

⟹ Percentage error in density is 4%.