Q: The density of a solid metal sphere is determined by measuring its mass and its diameter . The maximum error in the density of the sphere is (x/100) % . If the relative error in measuring the mass and the diameter are 6.0 % and 1.5 % respectively , the value of x is – – – –

Sol: Density , $\displaystyle \rho = \frac{M}{V}$

$\displaystyle \rho = \frac{M}{\frac{4}{3}\pi R^3}$

$\displaystyle \rho = \frac{M}{\frac{4}{3}\pi (D/2)^3}$

$\displaystyle \rho = \frac{M}{\frac{\pi}{6}D^3}$

$\displaystyle \frac{\Delta \rho}{\rho} \times 100 = (\frac{\Delta M}{M}\times 100 ) + 3 (\frac{\Delta D}{D}\times 100 ) $

= 6 % + 3(1.5 %) = 10.5 %

(x/100) % = 10.5 %

x = 1050