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Physics Question on Units and measurement

The density of the material of a cube can be estimated by measuring its mass and the length of one of its sides. If the maximum error in the measurement of mass and length are 0.3% and 0.2% respectively, the maximum error in the estimation of the density of the cube is approximately

A

0.011

B

0.005

C

0.009

D

0.007

Answer

0.009

Explanation

Solution

Density(ρ)==Mass(m)Volume(V)Density \left(\rho\right)= =\frac{Mass \left(m\right)}{Volume \left(V\right)}
∴(△ρρ)max=△mm+Δvv=Δmm+3ΔLL\therefore\left(\frac{\bigtriangleup\rho}{\rho}\right)_{max} =\frac{\bigtriangleup m}{m}+\frac{\Delta v}{v}=\frac{\Delta m}{m}+\frac{3\Delta L}{L}
V=L3V = L^{3}
[∵ΔVV=3ΔLL]\left[\because\frac{\Delta V}{V}= \frac{3\Delta L}{L}\right]
∴(Δρρ)max×100=⌊0.3+3(0.2)⌋%=0.9%\therefore\left(\frac{\Delta\rho}{\rho}\right)_{max} \times100 =\lfloor0.3+3\left(0.2\right)\rfloor\%_{=0.9\%}