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%
Click to See Answer :
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 %