Concept of Error analysis

Question

Find the maximum error in calculation of inertia of solid sphere.

Radius: !!2 m ± 5%!!

Mass: !!3 Kg ± 10% !!

a) !!+-5%!!

b) !!+-10%!!

c) !!+- 20%!!

d) !!+- 25%!!

Solution

The moment of inertia of a solid sphere about its central axis,

!!I = 2/5 MR^2!!

Given that, !!(DeltaR)/R xx100 = 5%!! and !!(DeltaM)/M xx100 = 10%!!

We have to calculate !!(DeltaI)/I xx 100!!

!! => (DeltaI)/I xx100 = (DeltaM)/M xx100 + 2(DeltaR)/R xx100 !!

!!=> (DeltaI)/I xx100 = 10 % + 2xx 5% !!

!! => (DeltaI)/I xx 100 = 20%!!

Therefore, option (c) is correct.