Screw gauge readings
Pitch $=0.5 \ mm$
Circular scale division $=50$
Main scale reading $=2.5 \ mm$
Least count $=\frac{0.5}{50}=0.01 \ mm$
Circular scale division reading $=2$ odivisions
Relative error $=2 \%$
So,
Then dimensions reading from screw gauge $=$ Diameter of a solid ball
S.G. Reading $=$ main scale reading $+\left(\frac{\text { pitch }}{\text { circular scale division }}\right) \times$ circular scale division reading
$\text { Diameter of solid ball }=2.5+\frac{0.5}{50} \times 20=2.7 \ mm$
As density $\rho=\frac{\text { mass }}{\text { Volume }}=\frac{M}{\frac{4 \pi}{3}\left(\frac{D}{2}\right)^3}$
The relative percentage error in the density is
$\frac{\Delta \rho}{\rho} \times 100=\left(\frac{\Delta M }{ M }+\frac{3 \Delta D }{ D }\right) \times 100$
$\% \text { error }=\left(\frac{\Delta M }{ M } \times 100+\frac{3 \Delta D }{ D }\right) \times 100$
$=\left(2+3 \times \frac{0.01}{2.7}\right) \times 100$
$=3.1 \%$
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