A rectangular metal slab of mass 33.333 g has its length 8.0 cm, breadth 5.0 cm and thickness 1mm. The mass is measured with accuracy up to 1 mg with a senstitive balance. The length and breadth are measured with a vernier calipers having a least count of 0.01 cm. The thickness is measured with a screwgauge of least count 0.01 mm. Calculate the percentage accuracy in density from above measurements.

Explanation

The percentage error itself gives us the percentage accuracy.
`d = ("mass"(M))/("length"(l) xx "breadth"(b) xx "height"(h)) = M/(l b h)`
`:.` The relative error is given by
`(Delta d)/(d) = ((Delta M)/(M)) + ((Delta l)/(l)) + ((Delta b)/(b)) + ((Delta h)/h)`
Given 1 = 8.0 cm and l = 0.01 cm,
b = 5.0 cm and `Delta b = 0.01 cm`
`h = 1 mm ` and `Delta h = 0.01 mm ` and
`M = 33.333 g and Delta M = 1 mg = 0.001 g`
Hence , `(Delta M)/(M ) = (0.001)/(33.333)`
`(Delta l)/(l) = (0.01)/(8.0) , (Delta b)/(b) = (0.01)/5 and (Delta h)/(h) = (0.01)/(l)`
The percentage error is error by
`((DeltaM)/(m) + (Delta l)/(l) + (Delta b)/(b) + (Delta h)/(h)) xx 100`
`=((0.001)/(33.333) + (0.01)/(8.0) + (0.01)/(5) + (0.01)/(1)) xx 100`
`= 0.003 + 0.125 + 0.2 + 1.0 = 1.328 . 1.328 ~= 1.3`
The percentage error is 1.3%.