Question

A physical quantity is represented by X = [MᵃLᵇT^-c]. If percentage error in the measurement of M,L and T are ∝%, β% and gamma% respectively, then maximum percentage error in measurement of X should be? (Given that ∝, β and gamma are very small)

1. (∝a - βb + gamma·c)%
2. (∝a +βb + gamma·c)%
3. (∝a - βb - gamma·c)%
4. (∝a + βb - gamma·c)%

Answer 1

Answer:

maximum percentage error is ( αa + βb - γc )% ∴ option (4) is correct

Explanation:

As we know that

percentage error = Δx/x × 100 )

diffrentiating ΔX then we get ,

ΔX/X × 100 = a×(ΔM/M *100 )+ b × (ΔL/L*100) - c× (ΔT/T×100)

But , given that, percentage error of M , L and T is α , β and γ respectively .

⟹ ( ΔX/X×100)= (aα + bβ- cγ)%

maximum percentage error in measurement of X is (aα + bβ - cγ)%

• ∴ Option(4) is correct