The relative density of a metal may be found by hanging a block of the metal from a spring balance a

Question

The relative density of a metal may be found by hanging a block of the metal from a spring balance and noting that in air the balance reads $5.00 \pm 0.05 \mathrm{~N}$ while in water it reads $4.00 \pm 0.05 \mathrm{~N}$. The relative density would be quoted as\

Professor PC Thomas Classes · Answer

Weight in air $=\mathrm{w}_{1}=5.00 \pm 0.05$ Weight in water $=\mathrm{w}_{2}=4.00 \pm 0.05$\ Loss of weight $=\mathrm{w}_{1}-\mathrm{w}_{2}=1.00 \pm 0.1$\ Relative density $=\frac{w_{1}}{w_{1}-w_{2}}=\frac{5.00 \pm 0.05}{1.00 \pm 0.1}$\ $=5.00 \pm\left(1 	imes \%ight.$ error inw $\mathrm{w}_{1}+1 	imes \%$ \%error in $\left.\mathrm{w}_{1}-\mathrm{w}_{2}ight)$\ $=5.00 \pm\left(1 	imes \frac{0.05}{50} 	imes 100+\frac{0.1}{1} 	imes 100ight)$\ $=5.00 \pm(1+10) \quad=5.00 \pm 11 \%$\