Question

In the density measurement of a cube, the mass and edge length are measured as $(10.00\pm 0.10kg)$ and $(0.10\pm 0.01m)$, respectively. The error in the measurement of density is

• A. $0.01g/c{m}^3$
• B. $0.10g/c{m}^3$
• C. $3.1g/c{m}^3$
• D. $0.07g/c{m}^3$

Answer 1

The correct option is C $3.1g/c{m}^3$

Given:
$m\pm \Delta m=(10.00\pm 0.10)kg$

$L\pm \Delta L=(0.10\pm 0.01)m$

As we know,
Density, $\rho =\frac{m}{v}...\left(i\right)$

Dimension of, $\rho =\frac{M}{L^3}=M{L}^{-3}$

Maximum $\%$ error in measurement of cube will be given by

$\frac{\Delta \rho }{\rho }\times 100=(\frac{\Delta m}{m}\times 100+3(\frac{\Delta L}{L})\times 100)...\left(ii\right))$

Therefore, by putting the values in (ii) equation we get,

$\frac{\Delta \rho }{\rho }\times 100=\left(\frac{0.10}{10}\right)\times 100+3\left(\frac{0.01}{0.10}\right)\times 100$

$\Delta \rho =3100kg/m^3$

$\Delta \rho =3.1g/m^3$

Final Answer: (b)