In an experiment on determining density of a rectangular block, the dimensions of the block are mesured with vernier callipers `(V.C = 0.01 cm)` and its mass is measured with a beam balance `(L.C. = 0.1 g)`. The measured values are :
Mass`(m) = 39.3` g
Length`(l) = 5.12` cm
Breadth`(b) = 2.56` cm
Thickness`(t)=0.37` cm
Calculate density of the block with permissible limits of error.

Explanation

Density `(rho)= ("Mass")/("Volume")=m/(lxxbxxt)`
`=39.3/(5.12xx2.56xx0.37)g cm^(-3)`
`=8.1037 g cm^(-3)`
`=8.1 g cm^(-3)` (rounding off the result)
The maximum relative error in the density is given by
`(Delta rho)/rho=(Delta m)/m+(Delta l)/(l)+(Delta b)/b+(Delta t)/t`
`=0.1/39.3+0.01/5.12+0.01/2.56+0.01/0.37`
`=0.0024+0.0019+0.0039+0.027`
`=0.0358`
`:. " "Delta rho =0.0358 rho=0.0358xx8.1037 cong 0.3 g cm^(-3)`
Thus, the density of the solid is `(8.1 pm 0.3)g cm^(-3)`
Note : The main contribution to the relative error comes from the measurement of thickness (t). Hence, precision in the measurement of density can be increased by measuring thickness with screw gauge (L.C. = 0.001 cm) instead of vernier callipers (V.C. = 0.01 cm). experimentalists keep such facts in mind while carrying out different measurements in a given experiment.