devarshi-dt-logo

Question:

In the density measurement of a cube, the mass and edge length are measured as (10.00±0.10) kg and (0.10±0.01) m, respectively. The error in the measurement of density:

0.31kg/m^3

No answer

0.10kg/m^3

0.07kg/m^3

0.01kg/m^3

Solution:

Correct option is E. No answer
ρ = m/v
Δρ/ρ × 100% = Δm/m × 100% + 3(ΔL/L) × 100%(i)
which is only possible when error is small which is not the case in this question
Yet if we apply equation (i) we get
Δρ = 3100kg/m^3
Now we will calculate error, without using approximation
ρ_min = m_min/v_max = 9.9 / (0.11)^3 = 7438kg/m^3
and ρ_max = m_max/v_min = 10.1 / (0.09)^3 = 13854kg/m^3
Δρ = 6416.6kg/m^3
No option is matching