Question

02 points Previous Answers SerPSE9 1P052. The radius of a solid sphere is measured to be (6.30 ± 0.25) cm, and its mass is measured to be (1.70± 0.04 (Use the correct number of significant figures. Use the following formula to calculate the uncertainty in the density: 40- 43) My Nates Ask Your ) kg. Determine the density of the sphere in kilograms per cubic meter and the uncertainty in the density. Iculationst) x 103 kg/m2 Your response differs from the cor Ente r a number with the correct number of significant figures Need Help?Read lt Submit Answerl Save ProgressPractice Another Version Submit AssignmentSae Assigriment 259 PM 116/2019

Answer 1

The radius of the sphere is given by

$r\pm \Delta r = (6.30\pm 0.25)~cm$
And the mass of the sphere is given by

  $m\pm \Delta m = (1.70\pm 0.04)~kg$
And the density of the sphere is given by
   $\rho=\frac{m}{V}=\frac{m}{\frac{4}{3}\pi r^3}$
And putting the given values, we get
   $\rho=\frac{1.70}{\frac{4}{3}\pi \times (6.30\times 10^{-2})^3}$
$\Rightarrow \rho=1623.075~kg/m^3$
And the uncertainty is given by
   $\frac{\Delta \rho}{\rho}=\bigg|\frac{\Delta m}{m}\bigg|+3\bigg|\frac{\Delta r}{r}\bigg|$
So, putting the given values, we get
   $\frac{\Delta \rho}{\rho}=\frac{0.04}{1.70}+3\times \frac{0.25}{6.30}$
  $\Rightarrow \frac{\Delta \rho}{\rho}=0.14258$
$\Rightarrow \Delta \rho=0.14258\times 1623.075$
$\Rightarrow \Delta \rho=231.413~kg/m^3$
So, the density and its uncertainty is given by
   $\rho\pm \Delta \rho=(1623.075\pm 231.413)~kg/m^3$