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)/(lbh)`
`therefore` The relative error is given by
`(Delta d)/(d) = ((Delta M)/(M)) + ((Delta l)/(l)) + ((Delta b)/(b)) + ((Delta h)/(h))`
Given 1= 8.0cm and `Delta l= 0.01cm`
b=5.0cm and `Delta b= 0.01cm`
`h= 1mm and Delta h= 0.01mm and M= 33.333g and Delta M= 1mg= 0.001g`
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 given by
`((Delta M)/(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%