d
\(\,{l}\,\, = \,\,(4.00\,\, \pm \,\,0.01\,\,)\,cm\)   \(\therefore l\) ના માપનમાં આંશિક ત્રુટિ \( = \,\,\,\frac{{\Delta {l}}}{{l}}\, = \,\frac{{0.01}}{{4.0}}\, = \,0.0025\)

\(r\,\, = \,\,(0.250\,\, \pm \,\,0.001\,)\,\,cm\,\,\)     \(\therefore R\) ના માપનમાં આંશિક ત્રુટિ  \( = \,\,\,\,\frac{{\Delta r}}{r}\, = \,\frac{{0.001}}{{0.250}}\, = \,0.004\)

 \(m\,\, = \,\,(6.25\,\, \pm \,\,0.01)\,\,g\,\,\,\,\)   \(\therefore M\) ના માપનમાં આંશિક ત્રુટિ  \( = \,\,\,\,\frac{{\Delta m}}{m} = \frac{{0.01}}{{6.25}}\, = \,0.0016\)

ઘનતા = દળ /કદ  \( = \,\,\frac{m}{{\pi {r^2}{l}}}\,\) પરથી દ્રાવ્યની ઘનતામાં આંશિક ત્રુટિ  \( = \,\,\frac{{\Delta \rho }}{\rho }\, = \,\frac{{\Delta m}}{m}\, + \,\frac{{2\Delta r}}{r} = \frac{{\Delta {l}}}{{l}}\)

પ્રતિશત ત્રુટિ  \(\, = \,\frac{{\Delta \rho }}{\rho } \times \,100\,\% \) \( = \left( {\frac{{\Delta m}}{m} \times \,100} \right)\%  + \) \(2\left( {\frac{{\Delta r}}{r} \times 100} \right)\%  + \left( {\frac{{\Delta {l}}}{{l}} \times \,100} \right)\% \)

\( = \,(0.0025\, \times \,100)\,\% \,\, + \,\,2(0.004\, \times \,100)\% \,\, + \,\,(0.0016\, \times 100)\,\% \)

\(\, = \,0.25\% \, + \,0.8\%  + \,0.16\,\%  = \,1.21\% \)