Q: The density of a cube is measured by measuring its mass and length of its sides. If the maximum error in the measurement of mass and length are 4 % and 3 % respectively, the maximum error in the measurement of density will be

(a) 7%

(b) 9%

(c) 12%

(d) 13%

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Ans: (d)

Sol: Density = Mass/Volume

$\displaystyle \rho = \frac{M}{L^3} $

$\displaystyle \frac{\Delta \rho}{\rho} \times 100 = (\frac{\Delta M}{M} + 3 \frac{\Delta L}{L})100 $

$\displaystyle \frac{\Delta \rho}{\rho} \times 100 = (4 + 3 \times 3 ) $

= 13 %