Question

The density of a cube is found by measuring its mass and the length of its side. If the maximum errors in the measurement of mass and length are $$0.3\%$$ and $$0.2\%$$ respectively, the maximum error in the measurement of density is:

A
0.3%
B
0.5%
C
0.9%
D
1.1%

Solution

The correct option is C $$0.9\%$$Given that, Mass error $$m$$%=$$0.3$$% Length error $$l$$%=$$0.2$$%    We know that, Density = mass/ volume   $$\rho =\dfrac{M}{V}$$  $$\rho =\dfrac{M}{{{l}^{3}}}$$ Now, the percentage error is   $$\dfrac{\Delta \rho }{\rho }\times 100=\left[ \dfrac{\Delta m}{m}\times 100 \right]+3\left[ \dfrac{\Delta l}{l}\times 100 \right]$$ $$\dfrac{\Delta \rho }{\rho }\times 100=0.3$$%$$+\left( 3\times 0.2 \right)$$%   $$\dfrac{\Delta \rho }{\rho }\times 100=0.3$$%$$+0.6$$%  $$\dfrac{\Delta \rho }{\rho }\times 100=0.9$$% Hence, the maximum error in the measurement of density is $$0.9$$%Physics

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