A metal wire has mass (0.4 ± 0.002)g, radius (0.3 ± 0.001)mm and length (5 ± 0.02)cm. The maximum possible percentage error in the measurement of density will nearly be:

1.6%

$\text{Density of the wire is } d = \frac{M}{V} = \frac{M}{\pi R^2 L} $

$\text{fractional Error in density is } \frac{\Delta d}{d} = \frac{\Delta M}{M} + \frac{2\Delta R}{R} + \frac{\Delta L}{L} = \frac{0.002}{0.4} + 2\times \frac{0.001}{0.3}+ \frac{0.02}{5} = 0.005+2\times 0.0033+0.004 = 0.0016$

$\text{Percentage Error is } 0.0016\times 100\% = 1.6\%$