Question

A wire has a mass $0.3\pm 0.003g$, radius $0.5\pm 0.005mm$ and length $6\pm 0.06cm$. The maximum percentage error in the measurment of its density is

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is D $4$

We know that,

The density is $\rho =\frac{m}{V}$

For a cylinder it becomes

$\rho =\frac{m}{(\pi \times r^2\times l)}$

Relative percent errors for-

For mass

$m=\frac{0.003}{0.3}\times 100$

$m=1$

For radius

$r^2=\frac{2\times 0.005}{0.5}\times 100$

$r^2=2$

For length

$L=\frac{0.06}{6}\times 100$

$L=1$

Now,

The maximum percentage error in density

$\rho$ % = $m$ % + $r$ % + $L$ %

$\rho$ % =$1$ % + $2$ % + $1$ %

$\rho$ % = $4$ %

Hence, the maximum percentage error in the density is $4$