UPSEE 2019 Solved Paper

Here, mass of wire, m=(0.1±0.001)g
Radius, r=(0.5±0.005)mm and length,
L=(10±0.1)cm
As density of a wire,
ρ=

mass

volume

=

mass

area × length

⇒ρ=

m

πR2×L

So relative error in density,
±

Δρ

ρ

=±[

Δm

m

+2

ΔR

R

+

ΔL

L

]
⇒

Δρ

ρ

=

0.001×10−3

0.1×10−3

+2×

0.005×10−3

0.5×10−3

+

0.1×10−2

10×10−2

⇒

Δρ

ρ

=0.01+0.02+0.01
⇒

Δρ

ρ

=0.04
Maximum percentage error=

Δρ

ρ

×100=0.04×100=4%
Hence, the maximum percentage error in the measurement of density is 4%.