Question

how to calculate uncertainty in density of sphere? given radius (6.50+-0.20)cm and it's mass (1.85+-0.02)kg?? please help me... tq (:

Answer 1

Density is\[\rho = { m \over V}\]

Using Klein-McClintock uncertainty formula\[\omega = \sqrt{ \left( {\partial \rho \over \partial m} \omega(m) \right)^2 + \left( {\partial \rho \over \partial V} \omega(V) \right)^2}\]

The partial derivative of density with respect to m is 1/V.
The partial derivative of density with respect to V is -(m over V^2)

Therefore, we have\[\omega = \sqrt{ \left ( {1 \over V} 0.02 \right)^2 + \left( { \left( m \over V^2 \right)} 0.2 \right)^2}\] Substitute the values given for volume and mass into the equation.